Chapter 11, Problem 1P

Compute the total cost for each aggregate plan using these unit costs:

Regular output = $40

Overtime = $50

Subcontract = $60

Average Balance Inventory = $10

a.

b.

c. (Refer to part b) After complaints from some workers about working overtime every month during the first half of the year, the manager is now considering adding some temporary workers for the second half of the year, which would increase regular output to a steady 350 units a month, not using any overtime, and using subcontracting to make up needed output. Determine the total cost of that plan.

Summary Introduction

To compute: The total cost for each aggregate plan

Introduction: The aggregate plan is the output of sales and operations planning. The major concern of aggregate planning is the production time and quantity for the intermediate future. Aggregate planning would encompass a time prospect of approximately 3 to 18 months.

Answer to Problem 1P

The total cost for the aggregate plan is $78,600.

Explanation of Solution

Given information:

Regular output is $40, overtime is $50, subcontract is $60, and average balance inventory is $10.

In addition to this, the following information is given:

Month	January	February	March	April	May	June
Forecast	300	320	320	340	320	320
Regular	300	300	300	300	300	300
Overtime	20	20	20	20	20	20
Subcontract	0	0	0	0	0	0

Determine the aggregate plan to compute total cost:

Month		January	February	March	April	May	June	Total
Forecast		300	320	320	340	320	320	1,920
Output
Regular		300	300	300	300	300	300	1,800
Part-time
Overtime		20	20	20	20	20	20	120
Subcontract		0	0	0	0	0	0	0
Difference		20	0	0	-20	0	0	0
Inventory
Beginning		0	20	20	20	0	0	60
Ending		20	20	20	0	0	0	60
Average		10	20	20	10	0	0	60
Backlog		0	0	0	0	0	0	0
Costs
Regular	40	$12,000	$12,000	$12,000	$12,000	$12,000	$12,000	$72,000
Part-time
Overtime	50	$1,000	$1,000	$1,000	$1,000	$1,000	$1,000	$6,000
Subcontract	60	$0	$0	$0	$0	$0	$0	$0
Hire/Layoff
Inventory	10	$100	$200	$200	$100	$0	$0	$600
Backorders		$0	$0	$0	$0	$0	$0	$0
		$13,100	$13,200	$13,200	$13,100	$13,000	$13,000	$78,600

Supporting calculation:

Forecast, regular time units, overtime, and subcontract units were given.

Calculate the difference of month January:

It is the calculation of difference between forecast and output. Hence, it can be calculated by subtracting the forecast from the output. Hence, the difference is 20 units.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overtime}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(300+20+0\right)-300\\ =20\end{array}$

Calculate the difference of month February:

It is the calculation of difference between forecast and output. Hence, it can be calculated by subtracting the forecast from the output. Hence, the difference is 0 units.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overtime}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(300+20+0\right)-320\\ =0\end{array}$

Calculate the difference of month March:

It is the calculation of difference between forecast and output. Hence, it can be calculated by subtracting the forecast from the output. Hence, the difference is 0 units.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overtime}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(300+20+0\right)-320\\ =0\end{array}$

Note: The calculation repeats for all the months.

Beginning inventory:

The initial inventory is given as 0. For the remaining months, ending inventory of previous month would be the beginning inventory of present month.

Ending inventory for the month of January:

Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 20 units.

$\begin{array}{c}\text{Ending inventory}=\left[\begin{array}{l}\text{Beginning inventory of January}+\\ \text{Difference between output and forecast}\end{array}\right]\\ =0+20\\ =20\end{array}$

Ending inventory for the month of February:

Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 20 units.

$\begin{array}{c}\text{Ending inventory}=\left[\begin{array}{l}\text{Beginning inventory of February}+\\ \text{Difference between output and forecast}\end{array}\right]\\ =20+0\\ =20\end{array}$

Ending inventory for the month of March:

Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 20 units.

$\begin{array}{c}\text{Ending inventory}=\text{Beginning inventory of March}+\text{Difference between output and forecast}\\ =20+0\\ =20\end{array}$

Note: The calculation repeats for all the months.

Average inventory for the month of January:

It is calculated by taking an average of beginning inventory and ending inventory. Hence, the average inventory is 10 units.

$\begin{array}{c}\text{Average inventory}=\frac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\ =\frac{0+20}{2}\\ =10\end{array}$

Average inventory for the month of February:

It is calculated by taking an average of beginning inventory and ending inventory. Hence, the average inventory is 20 units.

$\begin{array}{c}\text{Average inventory}=\frac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\ =\frac{20+20}{2}\\ =20\end{array}$

Average inventory for the month of March:

It is calculated by taking an average of beginning inventory and ending inventory. Hence, the average inventory is 20 units.

$\begin{array}{c}\text{Average inventory}=\frac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\ =\frac{20+20}{2}\\ =20\end{array}$

Note: The calculation repeats for all the months.

Calculate the regular time cost for the month of January:

Regular time cost per unit is given as $40 and regular time unit is given as 300. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $12,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$40\times 300\\ =\$12,000\end{array}$

Calculate the regular time cost for the month of February:

Regular time cost per unit is given as $40 and regular time unit is given as 300. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $12,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$40\times 300\\ =\$12,000\end{array}$

Calculate the regular time cost for the month of March:

Regular time cost per unit is given as $40 and regular time unit is given as 300. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $12,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$40\times 300\\ =\$12,000\end{array}$

Note: The calculation repeats for all the months.

Calculate the total regular time cost:

It is calculated by adding the regular time cost of all the months.

$\begin{array}{c}\text{Total regular time cost}=\text{Regular time of all the months}\\ =\$12,000+\$12,000+\$12,000+\$12,000+\$12,000+\$12,000\\ =\$72,000\end{array}$

Hence, the total regular time cost is $72,000.

Calculate the overtime cost for the month of January:

Overtime cost per unit is given as $50 and overtime unit is given as 20. Overtime cost is calculated by multiplying overtime unit and overtime cost per unit. Hence, the overtime cost is $1,000.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$50\times 20\\ =\$1,000\end{array}$

Calculate the overtime cost for the month of February:

Overtime cost per unit is given as $50 and overtime unit is given as 20. Overtime cost is calculated by multiplying overtime unit and overtime cost per unit. Hence, the overtime cost is $1,000.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$50\times 20\\ =\$1,000\end{array}$

Calculate the overtime cost for the month of March:

Overtime cost per unit is given as $50 and overtime unit is given as 20. Overtime cost is calculated by multiplying overtime unit and overtime cost per unit. Hence, the overtime cost is $1,000.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$50\times 20\\ =\$1,000\end{array}$

Note: The calculation repeats for all the months.

Calculate the total overtime cost:

It is calculated by adding the overtime cost of all the months.

$\begin{array}{c}\text{Total overtime cost}=\text{Overtime of all the months}\\ =\$1,000+\$1,000+\$1,000+\$1,000+\$1,000+\$1,000\\ =\$6,000\end{array}$

Hence, the total overtime cost is $6,000.

Calculate the subcontract cost for the month of January:

Subcontract cost per unit is given as $60 and subcontract unit is given as 0. Subcontract cost is calculated by multiplying subcontract unit and subcontract cost per unit. Hence, the subcontract cost is $0.

$\begin{array}{c}\text{Subcontract cost}=\text{Subcontract cost per unit}\times \text{Subcontract units}\\ =\$60\times 0\\ =\$0\end{array}$

Calculate the subcontract cost for the month of February:

Subcontract cost per unit is given as $60 and subcontract unit is given as 0. Subcontract cost is calculated by multiplying subcontract unit and subcontract cost per unit. Hence, the subcontract cost is $0.

$\begin{array}{c}\text{Subcontract cost}=\text{Subcontract cost per unit}\times \text{Subcontract units}\\ =\$60\times 0\\ =\$0\end{array}$

Calculate the subcontract cost for the month of March:

Subcontract cost per unit is given as $60 and subcontract unit is given as 0. Subcontract cost is calculated by multiplying subcontract unit and subcontract cost per unit. Hence, the subcontract cost is $0.

$\begin{array}{c}\text{Subcontract cost}=\text{Subcontract cost per unit}\times \text{Subcontract units}\\ =\$60\times 0\\ =\$0\end{array}$

Note: The calculation repeats for all the months.

Calculate the total subcontract cost:

It is calculated by adding the subcontract cost of all the months.

$\begin{array}{c}\text{Total subcontract cost}=\text{Subcontract of all the months}\\ =\$0+\$0+\$0+\$0+\$0+\$0\\ =\$0\end{array}$

Hence, the total subcontract cost is $0.

Calculate the inventory cost for the month of January:

It is calculated by average balance inventory cost and the average inventory units. Hence, the inventory cost is $100.

$\begin{array}{c}\text{Inventory cost}=\text{Inventory cost per unit}\times \text{Average inventory}\\ =\$10\times 10\\ =\$100\end{array}$

Calculate the inventory cost for the month of February:

It is calculated by average balance inventory cost and the average inventory units. Hence, the inventory cost is $200.

$\begin{array}{c}\text{Inventory cost}=\text{Inventory cost per unit}\times \text{Average inventory}\\ =\$10\times 20\\ =\$200\end{array}$

Calculate the inventory cost for the month of March:

It is calculated by average balance inventory cost and the average inventory units. Hence, the inventory cost is $200.

$\begin{array}{c}\text{Inventory cost}=\text{Inventory cost per unit}\times \text{Average inventory}\\ =\$10\times 20\\ =\$200\end{array}$

Note: The calculation repeats for all the months.

Calculate the total inventory cost:

It is calculated by adding the inventory cost of all the months.

$\begin{array}{c}\text{Total inventory cost}=\text{Inventory cost of all the months}\\ =\$100+\$200+\$200+\$100+\$0+\$0\\ =\$600\end{array}$

Hence, the total inventory cost is $600.

Calculate the total cost of the plan:

It is calculated by adding the total regular time cost, overtime cost, subcontract cost, and inventory cost.

$\begin{array}{c}\text{Total cost of the plan}=\left(\begin{array}{l}\text{Total regular time cost}+\text{Total overtime cost}+\\ \text{Total subcontract cost}+\text{Total inventory cost}\end{array}\right)\\ =\$72,000+\$6,000+\$0+\$600\\ =\$78,600\end{array}$

Hence, the total cost of the plan is $78,600.

Summary Introduction

To compute: The total cost for each aggregate plan.

Introduction:The aggregate plan is the output of sales and operations planning. The major concern of aggregate planning is the production time and quantity for the intermediate future. Aggregate planning would encompass a time prospect of approximately 3 to 18 months.

Answer to Problem 1P

The total cost for the aggregate plan is $95,500.

Explanation of Solution

Given information:

Regular output is $40, overtime is $50, subcontract is $60, and average balance inventory is $10.

In addition to this, the following information is given:

Month	July	August	September	October	November	December
Forecast	320	340	360	380	400	400
Regular	300	300	300	300	300	300
Overtime	20	20	20	20	30	30
Subcontract	20	30	40	40	60	70

Determine the aggregate plan to compute total cost:

Month		July	August	September	October	November	December	Total
Forecast		320	340	360	380	400	400	2,200
Output
Regular		300	300	300	300	300	300	1,800
Part-time
Overtime		20	20	20	20	30	30	140
Subcontract		20	30	40	40	60	70	260
Difference		20	10	0	-20	-10	0	0
Inventory
Beginning		0	20	30	30	10	0	90
Ending		20	30	30	10	0	0	90
Average		10	25	30	20	5	0	90
Backlog		0	0	0	0	0	0	0
Costs
Regular	40	$12,000	$12,000	$12,000	$12,000	$12,000	$12,000	$72,000
Part-time
Overtime	50	$1,000	$1,000	$1,000	$1,000	$1,500	$1,500	$7,000
Subcontract	60	$1,200	$1,800	$2,400	$2,400	$3,600	$4,200	$15,600
Hire/Layoff
Inventory	10	$100	$250	$300	$200	$50	$0	$900
Backorders
		$14,300	$15,050	$15,700	$15,600	$17,150	$17,700	$95,500

Supporting calculation:

Forecast, regular time units, overtime, and subcontract units were given.

Calculate the difference of month July:

It is the calculation of difference between forecast and output. Hence, it can be calculated by subtracting the forecast from the output. Hence, the difference is 20 units.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overtime}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(300+20+20\right)-320\\ =20\end{array}$

Calculate the difference of month August:

It is the calculation of difference between forecast and output. Hence, it can be calculated by subtracting the forecast from the output. Hence, the difference is 10 units.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overtime}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(300+20+30\right)-340\\ =10\end{array}$

Calculate the difference of month September:

It is the calculation of difference between forecast and output. Hence, it can be calculated by subtracting the forecast from the output. Hence, the difference is 0 units.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overtime}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(300+20+40\right)-360\\ =0\end{array}$

Note: The calculation repeats for all the months.

Beginning inventory:

The initial inventory is given as 0. For the remaining months, ending inventory of previous month would be the beginning inventory of present month.

Ending inventory for the month of July:

Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 20 units.

$\begin{array}{c}\text{Ending inventory}=\text{Beginning inventory of July}+\text{Difference between output and forecast}\\ =0+20\\ =20\end{array}$

Ending inventory for the month of August:

Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 20 units.

$\begin{array}{c}\text{Ending inventory}=\text{Beginning inventory of August}+\text{Difference between output and forecast}\\ =20+10\\ =30\end{array}$

Ending inventory for the month of September:

Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 20 units.

$\begin{array}{c}\text{Ending inventory}=\text{Beginning inventory of September}+\text{Difference between output and forecast}\\ =30+0\\ =30\end{array}$

Note: The calculation repeats for all the months.

Average inventory for the month of July:

It is calculated by taking an average of beginning inventory and ending inventory. Hence, the average inventory is 10 units.

$\begin{array}{c}\text{Average inventory}=\frac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\ =\frac{0+20}{2}\\ =10\end{array}$

Average inventory for the month of August:

It is calculated by taking an average of beginning inventory and ending inventory. Hence, the average inventory is 25 units.

$\begin{array}{c}\text{Average inventory}=\frac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\ =\frac{20+30}{2}\\ =25\end{array}$

Average inventory for the month of September:

It is calculated by taking an average of beginning inventory and ending inventory. Hence, the average inventory is 30 units.

$\begin{array}{c}\text{Average inventory}=\frac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\ =\frac{30+30}{2}\\ =30\end{array}$

Note: The calculation repeats for all the months.

Calculate the regular time cost for the month of July:

Regular time cost per unit is given as $40 and regular time unit is given as 300. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $12,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$40\times 300\\ =\$12,000\end{array}$

Calculate the regular time cost for the month of August:

Regular time cost per unit is given as $40 and regular time unit is given as 300. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $12,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$40\times 300\\ =\$12,000\end{array}$

Calculate the regular time cost for the month of September:

Regular time cost per unit is given as $40 and regular time unit is given as 300. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $12,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$40\times 300\\ =\$12,000\end{array}$

Note: The calculation repeats for all the months.

Calculate the total regular time cost:

It is calculated by adding the regular time cost of all the months.

$\begin{array}{c}\text{Total regular time cost}=\text{Regular time of all the months}\\ =\$12,000+\$12,000+\$12,000+\$12,000+\$12,000+\$12,000\\ =\$72,000\end{array}$

Hence, the total regular time cost is $72,000.

Calculate the overtime cost for the month of July:

Overtime cost per unit is given as $50 and overtime unit is given as 20. Overtime cost is calculated by multiplying overtime unit and overtime cost per unit. Hence, the overtime cost is $1,000.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$50\times 20\\ =\$1,000\end{array}$

Calculate the overtime cost for the month of August:

Overtime cost per unit is given as $50 and overtime unit is given as 20. Overtime cost is calculated by multiplying overtime unit and overtime cost per unit. Hence, the overtime cost is $1,000.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$50\times 20\\ =\$1,000\end{array}$

Calculate the overtime cost for the month of September:

Overtime cost per unit is given as $50 and overtime unit is given as 20. Overtime cost is calculated by multiplying overtime unit and overtime cost per unit. Hence, the overtime cost is $1,000.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$50\times 20\\ =\$1,000\end{array}$

Note: The calculation repeats for all the months.

Calculate the total overtime cost:

It is calculated by adding the overtime cost of all the months.

$\begin{array}{c}\text{Total overtime cost}=\text{Overtime of all the months}\\ =\$1,000+\$1,000+\$1,000+\$1,000+\$1,000+\$1,000\\ =\$6,000\end{array}$

Hence, the total overtime cost is $6,000.

Calculate the subcontract cost for the month of July:

Subcontract cost per unit is given as $60 and subcontract unit is given as 20. Subcontract cost is calculated by multiplying subcontract unit and subcontract cost per unit. Hence, the subcontract cost is $1,200.

$\begin{array}{c}\text{Subcontract cost}=\text{Subcontract cost per unit}\times \text{Subcontract units}\\ =\$60\times 20\\ =\$1,200\end{array}$

Calculate the subcontract cost for the month of August:

Subcontract cost per unit is given as $60 and subcontract unit is given as 30. Subcontract cost is calculated by multiplying subcontract unit and subcontract cost per unit. Hence, the subcontract cost is $1,800.

$\begin{array}{c}\text{Subcontract cost}=\text{Subcontract cost per unit}\times \text{Subcontract units}\\ =\$60\times 30\\ =\$1,800\end{array}$

Calculate the subcontract cost for the month of September:

Subcontract cost per unit is given as $60 and subcontract unit is given as 40. Subcontract cost is calculated by multiplying subcontract unit and subcontract cost per unit. Hence, the subcontract cost is $2,400.

$\begin{array}{c}\text{Subcontract cost}=\text{Subcontract cost per unit}\times \text{Subcontract units}\\ =\$60\times 40\\ =\$2,400\end{array}$

Note: The calculation repeats for all the months.

Calculate the total subcontract cost:

It is calculated by adding the subcontract cost of all the months.

$\begin{array}{c}\text{Total subcontract cost}=\text{Subcontract of all the months}\\ =\$1,200+\$1,800+\$2,400+\$2,400+\$3,600+\$4,200\\ =\$15,600\end{array}$

Hence, the total subcontract cost is $15,600.

Calculate the inventory cost for the month of July:

It is calculated by average balance inventory cost and the average inventory units. Hence, the inventory cost is $100.

$\begin{array}{c}\text{Inventory cost}=\text{Inventory cost per unit}\times \text{Average inventory}\\ =\$10\times 10\\ =\$100\end{array}$

Calculate the inventory cost for the month of August:

It is calculated by average balance inventory cost and the average inventory units. Hence, the inventory cost is $250.

$\begin{array}{c}\text{Inventory cost}=\text{Inventory cost per unit}\times \text{Average inventory}\\ =\$10\times 25\\ =\$250\end{array}$

Calculate the inventory cost for the month of September:

It is calculated by average balance inventory cost and the average inventory units. Hence, the inventory cost is $300.

$\begin{array}{c}\text{Inventory cost}=\text{Inventory cost per unit}\times \text{Average inventory}\\ =\$10\times 30\\ =\$300\end{array}$

Note: The calculation repeats for all the months.

Calculate the total inventory cost:

It is calculated by adding the inventory cost of all the months.

$\begin{array}{c}\text{Total inventory cost}=\text{Inventory cost of all the months}\\ =\$100+\$250+\$300+\$200+\$50+\$0\\ =\$900\end{array}$

Hence, the total inventory cost is $900.

Calculate the total cost of the plan:

It is calculated by adding the total regular time cost, overtime cost, subcontract cost, and inventory cost.

$\begin{array}{c}\text{Total cost of the plan}=\left(\begin{array}{l}\text{Total regular time cost}+\text{Total overtime cost}+\\ \text{Total subcontract cost}+\text{Total inventory cost}\end{array}\right)\\ =\$72,000+\$6,000+\$15,600+\$900\\ =\$95,500\end{array}$

Hence, the total cost of the plan is $95,500.

Summary Introduction

To compute: The total cost for each aggregate plan.

Introduction:The aggregate plan is the output of sales and operations planning. The major concern of aggregate planning is the production time and quantity for the intermediate future. Aggregate planning would encompass a time prospect of approximately 3 to 18 months.

Answer to Problem 1P

The total cost for the aggregate plan is $91,000.

Explanation of Solution

Given information:

Regular output is $40, overtime is $50, subcontract is $60, and average balance inventory is $10.

In addition to this, the following information is given:

Month	July	August	September	October	November	December
Forecast	320	340	360	380	400	400
Regular	350	350	350	350	350	350
Overtime	0	0	0	0	0	0

It is given that subcontract can be used whenever necessary.

Determine the aggregate plan to compute total cost:

Month		July	August	September	October	November	December	Total
Forecast		320	340	360	380	400	400	2,200
Output
Regular		350	350	350	350	350	350	2,100
Part-time
Overtime
Subcontract						50	50
Difference		30	10	-10	-30	0	0	0
Inventory
Beginning		0	30	40	30	0	0	100
Ending		30	40	30	0	0	0	100
Average		15	35	35	15	0	0	100
Backlog		0	0	0	0	0	0	0
Costs
Regular	40	$14,000	$14,000	$14,000	$14,000	$14,000	$14,000	$84,000
Part-time
Overtime	50	$0	$0	$0	$0	$0	$0	$0
Subcontract	60	$0	$0	$0	$0	$3,000	$3,000	$6,000
Hire/Layoff
Inventory	10	$150	$350	$350	$150	$0	$0	$1,000
Backorders		0	0	0	0	0	0	0
		$14,150	$14,350	$14,350	$14,150	$17,000	$17,000	$91,000

Supporting calculation:

Forecast, regular time units, overtime, and subcontract units were given.

Calculate the difference of month July:

It is the calculation of difference between forecast and output. Hence, it can be calculated by subtracting the forecast from the output. Hence, the difference is 30 units.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overtime}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(350+0+0\right)-320\\ =30\end{array}$

Calculate the difference of month August:

It is the calculation of difference between forecast and output. Hence, it can be calculated by subtracting the forecast from the output. Hence, the difference is 10 units.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overtime}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(350+0+0\right)-340\\ =10\end{array}$

Calculate the difference of month September:

It is the calculation of difference between forecast and output. Hence, it can be calculated by subtracting the forecast from the output. Hence, the difference is -10 units.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overtime}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(350+0+0\right)-360\\ =-10\end{array}$

Note: The calculation repeats for all the months.

Beginning inventory:

The initial inventory is given as 0. For the remaining months, ending inventory of previous month would be the beginning inventory of present month.

Ending inventory for the month of July:

Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 30 units.

$\begin{array}{c}\text{Ending inventory}=\text{Beginning inventory of July}+\text{Difference between output and forecast}\\ =0+30\\ =30\end{array}$

Ending inventory for the month of August:

Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 40 units.

$\begin{array}{c}\text{Ending inventory}=\text{Beginning inventory of August}+\text{Difference between output and forecast}\\ =30+10\\ =40\end{array}$

Ending inventory for the month of September:

Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 20 units.

$\begin{array}{c}\text{Ending inventory}=\text{Beginning inventory of September}+\text{Difference between output and forecast}\\ =40+\left(-10\right)\\ =30\end{array}$

Note: The calculation repeats for all the months.

Average inventory for the month of July:

It is calculated by taking an average of beginning inventory and ending inventory. Hence, the average inventory is 15 units.

$\begin{array}{c}\text{Average inventory}=\frac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\ =\frac{0+30}{2}\\ =15\end{array}$

Average inventory for the month of August:

It is calculated by taking an average of beginning inventory and ending inventory. Hence, the average inventory is 35 units.

$\begin{array}{c}\text{Average inventory}=\frac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\ =\frac{30+40}{2}\\ =35\end{array}$

Average inventory for the month of September:

It is calculated by taking an average of beginning inventory and ending inventory. Hence, the average inventory is 35 units.

$\begin{array}{c}\text{Average inventory}=\frac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\ =\frac{40+30}{2}\\ =35\end{array}$

Note: The calculation repeats for all the months.

Calculate the regular time cost for the month of July:

Regular time cost per unit is given as $40 and regular time unit is given as 350. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $14,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$40\times 350\\ =\$14,000\end{array}$

Calculate the regular time cost for the month of August:

Regular time cost per unit is given as $40 and regular time unit is given as 350. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $14,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$40\times 350\\ =\$14,000\end{array}$

Calculate the regular time cost for the month of September:

Regular time cost per unit is given as $40 and regular time unit is given as 350. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $14,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$40\times 350\\ =\$14,000\end{array}$

Note: The calculation repeats for all the months.

Calculate the total regular time cost:

It is calculated by adding the regular time cost of all the months.

$\begin{array}{c}\text{Total regular time cost}=\text{Regular time of all the months}\\ =\$14,000+\$14,000+\$14,000+\$14,000+\$14,000+\$14,000\\ =\$84,000\end{array}$

Hence, the total regular time cost is $84,000.

Calculate the overtime cost for the month of July:

Overtime cost per unit is given as $50 and overtime unit is given as 0. Overtime cost is calculated by multiplying overtime unit and overtime cost per unit. Hence, the overtime cost is $0.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$50\times 20\\ =\$0\end{array}$

Calculate the overtime cost for the month of August:

Overtime cost per unit is given as $50 and overtime unit is given as 0. Overtime cost is calculated by multiplying overtime unit and overtime cost per unit. Hence, the overtime cost is $0.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$50\times 20\\ =\$0\end{array}$

Calculate the overtime cost for the month of September:

Overtime cost per unit is given as $50 and overtime unit is given as 0. Overtime cost is calculated by multiplying overtime unit and overtime cost per unit. Hence, the overtime cost is $0.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$50\times 20\\ =\$0\end{array}$

Note: The calculation repeats for all the months.

Calculate the total overtime cost:

It is calculated by adding the overtime cost of all the months.

$\begin{array}{c}\text{Total overtime cost}=\text{Overtime of all the months}\\ =\$0+\$0+\$0+\$0+\$0+\$0\\ =\$0\end{array}$

Hence, the total overtime cost is $0.

Calculate the subcontract cost for the month of July:

Subcontract cost per unit is given as $60 and subcontract unit is given as 0. Subcontract cost is calculated by multiplying subcontract unit and subcontract cost per unit. Hence, the subcontract cost is $0.

$\begin{array}{c}\text{Subcontract cost}=\text{Subcontract cost per unit}\times \text{Subcontract units}\\ =\$60\times 0\\ =\$0\end{array}$

Calculate the subcontract cost for the month of August:

Subcontract cost per unit is given as $60 and subcontract unit is given as 0. Subcontract cost is calculated by multiplying subcontract unit and subcontract cost per unit. Hence, the subcontract cost is $0.

$\begin{array}{c}\text{Subcontract cost}=\text{Subcontract cost per unit}\times \text{Subcontract units}\\ =\$60\times 0\\ =\$0\end{array}$

Calculate the subcontract cost for the month of September:

Subcontract cost per unit is given as $60 and subcontract unit is given as 0. Subcontract cost is calculated by multiplying subcontract unit and subcontract cost per unit. Hence, the subcontract cost is $0.

$\begin{array}{c}\text{Subcontract cost}=\text{Subcontract cost per unit}\times \text{Subcontract units}\\ =\$60\times 0\\ =\$0\end{array}$

Note: The calculation repeats for all the months. As there are backlogs in the month of November and December, there would be 50 units of subcontracting in those months.

Calculate the total subcontract cost:

It is calculated by adding the subcontract cost of all the months.

$\begin{array}{c}\text{Total subcontract cost}=\text{Subcontract of all the months}\\ =\$0+\$0+\$0+\$0+\$3,000+\$3,000\\ =\$6,000\end{array}$

Hence, the total subcontract cost is $15,600.

Calculate the inventory cost for the month of July:

It is calculated by average balance inventory cost and the average inventory units. Hence, the inventory cost is $150.

$\begin{array}{c}\text{Inventory cost}=\text{Inventory cost per unit}\times \text{Average inventory}\\ =\$10\times 15\\ =\$150\end{array}$

Calculate the inventory cost for the month of August:

It is calculated by average balance inventory cost and the average inventory units. Hence, the inventory cost is $350.

$\begin{array}{c}\text{Inventory cost}=\text{Inventory cost per unit}\times \text{Average inventory}\\ =\$10\times 35\\ =\$350\end{array}$

Calculate the inventory cost for the month of September:

It is calculated by average balance inventory cost and the average inventory units. Hence, the inventory cost is $350.

$\begin{array}{c}\text{Inventory cost}=\text{Inventory cost per unit}\times \text{Average inventory}\\ =\$10\times 35\\ =\$350\end{array}$

Note: The calculation repeats for all the months.

Calculate the total inventory cost:

It is calculated by adding the inventory cost of all the months.

$\begin{array}{c}\text{Total inventory cost}=\text{Inventory cost of all the months}\\ =\$150+\$350+\$350+\$150+\$50+\$0\\ =\$1,000\end{array}$

Hence, the total inventory cost is $1,000.

Calculate the total cost of the plan:

It is calculated by adding the total regular time cost, overtime cost, subcontract cost, and inventory cost.

$\begin{array}{c}\text{Total cost of the plan}=\left(\begin{array}{l}\text{Total regular time cost}+\text{Total overtime cost}+\\ \text{Total subcontract cost}+\text{Total inventory cost}\end{array}\right)\\ =\$84,000+\$0+\$6,000+\$1,000\\ =\$91,000\end{array}$

Hence, the total cost of the plan is $91,000.