Chapter 11, Problem 4P

a. Given the following forecast and steady regular output of 550 every month, what total cost would result if overtime is limited to a maximum of 40 units a month, and subcontracting is limited to a maximum of 10 units a month? Unit costs are:

Regular output = $20

Overtime = $30

Subcontract = $25

Average Inventory = $10

Backlog = $18

b. Suppose now that backlogs are not allowed. Modify your plan from part a to accommodate that new condition as economically as possible. The limits on overtime and subcontracting remain the same.

Summary Introduction

To compute: The total cost of the aggregate plan with backlog

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 4P

The total cost for the aggregate plan is $70,800 (without considering overtime and subcontract).

Explanation of Solution

Given information:

Regular output is $20, overtime is $30, subcontract is $25, carrying cost is $10, backorder cost is $18, regular production is 550 units per month, maximum overtime unit is of 40 units, and maximum subcontract unit is 10 units.

In addition to this, the following information is given:

Month	1	2	3	4	5	6
Forecast	540	540	570	590	600	580

Determine the aggregate plan to compute total cost (without overtime and subcontracting units):

Month		1	2	3	4	5	6	Total
Forecast		540	540	570	590	600	580	3,420
Output
Regular		550	550	550	550	550	550	3,300
Part-time
Overtime
Subcontract
Difference		10	10	-20	-40	-50	-30	-120
Inventory
Beginning		0	10	20	0	0	0	0
Ending		10	20	0	0	0	0	0
Average		5	15	10	0	0	0	0
Backlog		0	0	0	40	90	120	250
Costs
Regular	20	$11,000	$11,000	$11,000	$11,000	$11,000	$11,000	$66,000
Part-time
Overtime	30	$0	$0	$0	$0	$0	$0	$0
Subcontract	25	$0	$0	$0	$0	$0	$0	$0
Hire/Layoff
Inventory	10	$50	$150	$100	$0	$0	$0	$300
Backorders	18	0	0	0	720	1620	2160	$4,518
		$11,050	$11,150	$11,100	$11,720	$12,620	$13,160	$70,800

Supporting calculation:

Forecast and regular time units were given.

Calculate the difference for the month of 1:

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 10units.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overtime}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(550+0+0\right)-540\\ =10\end{array}$

Calculate the difference for the month of 2:

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.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overtime}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(550+0+0\right)-540\\ =10\end{array}$

Calculate the difference for the month of 3:

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.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overtime}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(550+0+0\right)-570\\ =-20\end{array}$

Note: The calculation repeats for all the months.

Backlogs:

As the values of difference between output and forecast are negative, there would be backlogs.

Backlogs for first three months:

It is number of units required in the month. As the differences are non-negative values, the backlog would begin from 4^th month. Hence, the backlog for 1^st, 2^nd, and 3^rd month would be0 units.

Backlogs for the month of 4:

It is number of units required in the month. It is calculated by adding the backlog of previous month and the difference between output and forecast of current month. Hence, the backlog is 40 units.

$\begin{array}{c}\text{Backlogs}=\text{Backlog of previous month}+\text{Difference between output and forecast}\\ =0+40\\ =40\end{array}$

Backlogs for the month of 5:

It is number of units required in the month. It is calculated by adding the backlog of previous month and the difference between output and forecast of current month (without considering the negative sign). Hence, the backlog is 90 units.

$\begin{array}{c}\text{Backlogs}=\text{Backlog of previous month}+\text{Difference between output and forecast}\\ =40+50\\ =90\end{array}$

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 1^st month:

Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 10 units.

$\begin{array}{c}\text{Ending inventory}=\text{Beginning inventory of January}+\text{Difference between output and forecast}\\ =0+10\\ =10\end{array}$

Ending inventory for 2^nd month:

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

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

Ending inventory for 3^rd month:

Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 0 units.

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

Note: The calculation repeats for all the months.

Average inventory for 1^st month:

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

$\begin{array}{c}\text{Average inventory}=\frac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\ =\frac{0+10}{2}\\ =5\end{array}$

Average inventory for 2^nd month:

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

$\begin{array}{c}\text{Average inventory}=\frac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\ =\frac{10+20}{2}\\ =15\end{array}$

Average inventory for 3^rd month:

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

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

Note: The calculation repeats for all the months.

Calculate the regular time cost for the 1^st month:

Regular time cost per unit is given as $20 and regular time unit is given as 550. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $11,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$20\times 550\\ =\$11,000\end{array}$

Calculate the regular time cost for the 2^nd month:

Regular time cost per unit is given as $20 and regular time unit is given as 550. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $11,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$20\times 550\\ =\$11,000\end{array}$

Calculate the regular time cost for the 3^rdmonth:

Regular time cost per unit is given as $20 and regular time unit is given as 550. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $11,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$20\times 550\\ =\$11,000\end{array}$

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.

$\begin{array}{c}\text{Total regular time cost}=\text{Regular time of all the months}\\ =\$11,000+\$11,000+\$11,000+\$11,000+\$11,000+\$11,000\\ =\$66,000\end{array}$

Hence, the total regular time cost is $66,000.

Calculate the overtime cost for the 1^st month:

Overtime cost per unit is given as $30 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.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$30\times 0\\ =\$0\end{array}$

Calculate the overtime cost for the 2^nd month:

Overtime cost per unit is given as $30 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.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$30\times 0\\ =\$0\end{array}$

Calculate the overtime cost for the 3^rd month:

Overtime cost per unit is given as $30 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.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$30\times 0\\ =\$0\end{array}$

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 1^st month:

Subcontract cost per unit is given as $25 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.

$\begin{array}{c}\text{Subcontract cost}=\text{Subcontract cost per unit}\times \text{Subcontract units}\\ =\$25\times 0\\ =\$0\end{array}$

Calculate the subcontract cost for 2^nd month:

Subcontract cost per unit is given as $25 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.

$\begin{array}{c}\text{Subcontract cost}=\text{Subcontract cost per unit}\times \text{Subcontract units}\\ =\$25\times 0\\ =\$0\end{array}$

Calculate the subcontract cost for 3^rd month:

Subcontract cost per unit is given as $25 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.

$\begin{array}{c}\text{Subcontract cost}=\text{Subcontract cost per unit}\times \text{Subcontract units}\\ =\$25\times 0\\ =\$0\end{array}$

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 1^st month:

It is calculated by average balance inventory cost and the average inventory units. Hence, the inventory cost is $50.

$\begin{array}{c}\text{Inventory cost}=\text{Inventory cost per unit}\times \text{Average inventory}\\ =\$10\times 5\\ =\$50\end{array}$

Calculate the inventory cost for 2^nd month:

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 3^rd month:

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 total inventory cost:

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

$\begin{array}{c}\text{Total inventory cost}=\text{Inventory cost of all the months}\\ =\$50+\$150+\$100+\$0+\$0+\$0\\ =\$300\end{array}$

Hence, the total inventory cost is $300.

Calculate the backorder cost for first three months:

As there are no backlogs for first three months, there would not be backorder cost.

Calculate the backorder cost for 4^th month:

It is calculated by multiplying the backorder cost and the backlog. Hence, the backorder cost is $720.

$\begin{array}{c}\text{Backorder cost}=\text{Backorder cost per unit}\times \text{Backlogs}\\ =\$18\times 40\\ =\$720\end{array}$

Calculate the backorder cost for 5^th month:

It is calculated by multiplying the backorder cost and the backlog. Hence, the backorder cost is $1,620.

$\begin{array}{c}\text{Backorder cost}=\text{Backorder cost per unit}\times \text{Backlogs}\\ =\$18\times 90\\ =\$1,620\end{array}$

Note: The calculation repeats for all the months.

Calculate the total backorder cost:

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

$\begin{array}{c}\text{Total backorder cost}=\text{Backorder cost of all the months}\\ =\$0+\$0+\$0+\$720+\$1,620+\$2,160\\ =\$4,500\end{array}$

Hence, the total backorder cost is $4,500.

Calculate the total cost of the plan:

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

$\begin{array}{c}\text{Total cost of the plan}=\left(\begin{array}{l}\text{Total regular time cost}+\text{Total overtime cost}+\\ \text{Total subcontract cost}+\text{Total inventory cost}+\\ \text{Total backorder cost}\end{array}\right)\\ =\$66,000+\$0+\$0+\$300+\$4,500\\ =\$70,800\end{array}$

Hence, the total cost of the plan is $70,800.

Summary Introduction

To compute: The total cost of the aggregate plan if the backlog is not allowed

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 4P

The total cost for the aggregate plan is $69,750 (considering overtime and subcontract).

Explanation of Solution

Given information:

Regular output is $20, overtime is $30, subcontract is $25, carrying cost is $10, backorder cost is $18, regular production is 550 units per month, maximum overtime unit is of 40 units, and maximum subcontract unit is 10 units.

In addition to this, the following information is given:

Month	1	2	3	4	5	6
Forecast	540	540	570	590	600	580

Determine the total cost of the plan (considering overtime and subcontract):

Month		1	2	3	4	5	6	Total
Forecast		540	540	570	590	600	580	3,420
Output
Regular		550	550	550	550	550	550	3,300
Part-time
Overtime					30	40	20	90
Subcontract					10	10	10	30
Difference		10	10	-20	0	0	0	0
Inventory
Beginning		0	10	20	0	0	0	30
Ending		10	20	0	0	0	0	30
Average		5	15	10	0	0	0	30
Backlog		0	0	0	0	0	0	0
Costs
Regular	20	$11,000	$11,000	$11,000	$11,000	$11,000	$11,000	$66,000
Part-time
Overtime	30	$0	$0	$0	$900	$1,200	$600	$2,700
Subcontract	25	$0	$0	$0	$250	$250	$250	$750
Hire/Layoff
Inventory	10	$50	$150	$100	$0	$0	$0	$300
Backorders	18	0	0	0	0	0	0	$0
		$11,050	$11,150	$11,100	$12,150	$12,450	$11,850	$69,750

Supporting calculation:

Forecast and regular time units are given. It is given maximum units of overtime is 20 units and maximum subcontract unit is 10 units. The added units should make the difference from a negative value to 0.

Calculate the difference for the month of 1:

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.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overtime}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(550+0+0\right)-540\\ =10\end{array}$

Calculate the difference for the month of 2:

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.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overtime}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(550+0+0\right)-540\\ =10\end{array}$

Calculate the difference for the month of 3:

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.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overtime}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(550+0+0\right)-570\\ =-20\end{array}$

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 1^st month:

Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 10 units.

$\begin{array}{c}\text{Ending inventory}=\text{Beginning inventory of January}+\text{Difference between output and forecast}\\ =0+10\\ =10\end{array}$

Ending inventory for 2^nd month:

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

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

Ending inventory for 3^rd month:

Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 0 units.

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

Note: The calculation repeats for all the months.

Average inventory for 1^st month:

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

$\begin{array}{c}\text{Average inventory}=\frac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\ =\frac{0+10}{2}\\ =5\end{array}$

Average inventory for 2^nd month:

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

$\begin{array}{c}\text{Average inventory}=\frac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\ =\frac{10+20}{2}\\ =15\end{array}$

Average inventory for 3^rd month:

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

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

Note: The calculation repeats for all the months.

Calculate the regular time cost for the 1^st month:

Regular time cost per unit is given as $20 and regular time unit is given as 550. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $11,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$20\times 550\\ =\$11,000\end{array}$

Calculate the regular time cost for the 2^nd month:

Regular time cost per unit is given as $20 and regular time unit is given as 550. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $11,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$20\times 550\\ =\$11,000\end{array}$

Calculate the regular time cost for the 3^rdmonth:

Regular time cost per unit is given as $20 and regular time unit is given as 550. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $11,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$20\times 550\\ =\$11,000\end{array}$

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.

$\begin{array}{c}\text{Total regular time cost}=\text{Regular time of all the months}\\ =\$11,000+\$11,000+\$11,000+\$11,000+\$11,000+\$11,000\\ =\$66,000\end{array}$

Hence, the total regular time cost is $66,000.

Calculate the overtime cost for 1^st month:

Overtime cost per unit is given as $30 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.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$30\times 0\\ =\$0\end{array}$

Calculate the overtime cost for the 2^nd month:

Overtime cost per unit is given as $30 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.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$30\times 0\\ =\$0\end{array}$

Calculate the overtime cost for the 3^rd month:

Overtime cost per unit is given as $30 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.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$30\times 0\\ =\$0\end{array}$

Calculate the overtime cost for the 4^th month:

Overtime cost per unit is given as $30 and overtime unit is given as 30. Overtime cost is calculated by multiplying overtime unit and overtime cost per unit. Hence, the overtime cost is $900.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$30\times 30\\ =\$900\end{array}$

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.

$\begin{array}{c}\text{Total overtime cost}=\text{Overtime of all the months}\\ =\$0+\$0+\$0+\$900+\$1,200+\$600\\ =\$2,700\end{array}$

Hence, the total overtime cost is $2,700.

Calculate the subcontract cost for 1^st month:

Subcontract cost per unit is given as $25 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.

$\begin{array}{c}\text{Subcontract cost}=\text{Subcontract cost per unit}\times \text{Subcontract units}\\ =\$25\times 0\\ =\$0\end{array}$

Calculate the subcontract cost for 2^nd month:

Subcontract cost per unit is given as $25 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.

$\begin{array}{c}\text{Subcontract cost}=\text{Subcontract cost per unit}\times \text{Subcontract units}\\ =\$25\times 0\\ =\$0\end{array}$

Calculate the subcontract cost for 3^rd month:

Subcontract cost per unit is given as $25 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.

$\begin{array}{c}\text{Subcontract cost}=\text{Subcontract cost per unit}\times \text{Subcontract units}\\ =\$25\times 0\\ =\$0\end{array}$

Calculate the subcontract cost for 3^rd month:

Subcontract cost per unit is given as $25 and subcontract unit is given as 10. Subcontract cost is calculated by multiplying subcontract unit and subcontract cost per unit. Hence, the subcontract cost is $250.

$\begin{array}{c}\text{Subcontract cost}=\text{Subcontract cost per unit}\times \text{Subcontract units}\\ =\$25\times 10\\ =\$250\end{array}$

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.

$\begin{array}{c}\text{Total subcontract cost}=\text{Subcontract of all the months}\\ =\$0+\$0+\$0+\$250+\$250+\$250\\ =\$0\end{array}$

Hence, the total subcontract cost is $0.

Calculate the inventory cost for 1^st month:

It is calculated by average balance inventory cost and the average inventory units. Hence, the inventory cost is $50.

$\begin{array}{c}\text{Inventory cost}=\text{Inventory cost per unit}\times \text{Average inventory}\\ =\$10\times 5\\ =\$50\end{array}$

Calculate the inventory cost for 2^nd month:

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 3^rd month:

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 total inventory cost:

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

$\begin{array}{c}\text{Total inventory cost}=\text{Inventory cost of all the months}\\ =\$50+\$150+\$100+\$0+\$0+\$0\\ =\$300\end{array}$

Hence, the total inventory cost is $300.

Calculate the total cost of the plan:

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

$\begin{array}{c}\text{Total cost of the plan}=\left(\begin{array}{l}\text{Total regular time cost}+\text{Total overtime cost}+\\ \text{Total subcontract cost}+\text{Total inventory cost}\end{array}\right)\\ =\$66,000+\$2,700+\$750+\$300\\ =\$69,750\end{array}$

Hence, the total cost of the plan is $69,750.