Chapter 11, Problem 8P

Nowjuice, Inc., produces Shakewell^® fruit juice. A planner has developed an aggregate forecast for demand (in cases) for the next six months.

Use the following information to develop aggregate plans.

Develop an aggregate plan using each of the following guidelines and compute the total cost for each plan. Which plan has the lowest total cost? Note: Backlogs are not allowed.

a. Use level production. Supplement using overtime as needed.

b. Use a combination of overtime (500 cases per period maximum), inventory, and subcontracting (500 cases per period maximum) to handle variations in demand.

C. Use overtime up to 750 cases per period and inventory to handle variations in demand.

Summary Introduction

To determine: The total cost using level strategy of aggregate planning.

Introduction: Level production strategy is a production strategy used to produce at a constant rate. This strategy keeps constant level of workforce and backlog of demand.

Answer to Problem 8P

The total cost of the aggregate plan is $350,800.

Explanation of Solution

Given information:

Regular production cost is $10, overtime production cost is $16, subcontracting cost is $20, holding cost is $1, regular capacity is 5,000 units, and beginning inventory is given as 0 units. In addition to this forecast for 6 months is given as follows:

Month	July	June	July	August	September	October	Total
Forecast	4,000	4,800	5,600	7,200	6,400	5,000	33,000

Determine the total cost of the plan:

It is given that regular productions should be used. No backlogs are allowed. Supplements can be satisfied using overtime.

Supporting explanation:

Calculate the difference for the month of May:

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 1,000 units.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overitme}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(5,000+0+0\right)-4,000\\ =1,000\end{array}$

Calculate the difference for the month of June:

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 1,000 units.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overitme}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(5,000+0+0\right)-4,800\\ =200\end{array}$

Calculate the difference for the month of 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 -600 units.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overitme}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(5,000+0+0\right)-5,600\\ =-600\end{array}$

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 May:

Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 1,000 units.

$\begin{array}{c}\text{Ending inventory}=\text{Beginning inventory}+\text{Difference between output and forecast}\\ =0+1,000\\ =1,000\end{array}$

Ending inventory for the month of June:

Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 1,200 units.

$\begin{array}{c}\text{Ending inventory}=\text{Beginning inventory}+\text{Difference between output and forecast}\\ =1,000+200\\ =1,200\end{array}$

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 600 units.

$\begin{array}{c}\text{Ending inventory}=\text{Beginning inventory}+\text{Difference between output and forecast}\\ =1,200-600\\ =600\end{array}$

Note: The calculation repeats for all the months.

Average inventory for the month of May:

It is calculated by taking an average of beginning inventory and ending inventory. Hence, the average inventory is 500 units.

$\begin{array}{c}\text{Average inventory}=\frac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\ =\frac{0+1,000}{2}\\ =500\end{array}$

Average inventory for the month of June:

It is calculated by taking an average of beginning inventory and ending inventory. Hence, the average inventory is 1,100 units.

$\begin{array}{c}\text{Average inventory}=\frac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\ =\frac{1,000+1,200}{2}\\ =1,100\end{array}$

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 900 units.

$\begin{array}{c}\text{Average inventory}=\frac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\ =\frac{1,200+600}{2}\\ =900\end{array}$

Note: The calculation repeats for all the months.

Calculate the regular time cost for the month of May:

Regular time cost per unit is given as $10 and regular time unit is given as 5,000. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $50,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$10\times 5,000\\ =\$50,000\end{array}$

Calculate the regular time cost for the month of June:

Regular time cost per unit is given as $10 and regular time unit is given as 5,000. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $50,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$10\times 5,000\\ =\$50,000\end{array}$

Calculate the regular time cost for the month of July:

Regular time cost per unit is given as $10 and regular time unit is given as 5,000. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $50,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$10\times 5,000\\ =\$50,000\end{array}$

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.

$\begin{array}{c}\text{Total regular time cost}=\text{Regular time of all the months}\\ =\$50,000+\$50,000+\$50,000+\$50,000+\$50,000+\$50,000\\ =\$300,000\end{array}$

Hence, the total regular time cost is $300,000.

Calculate the overtime cost for the month of May:

Overtime cost per unit is given as $16 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.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$16\times 0\\ =\$0\end{array}$

Calculate the overtime cost for the month of June:

Overtime cost per unit is given as $16 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.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$16\times 0\\ =\$0\end{array}$

Calculate the overtime cost for the month of July:

Overtime cost per unit is given as $16 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.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$16\times 0\\ =\$0\end{array}$

Calculate the overtime cost for the month of August:

Overtime cost per unit is given as $16 and overtime unit is given as 1,600. Overtime cost is calculated by multiplying overtime unit and overtime cost per unit. Hence, the overtime cost is $25,600.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$16\times 16,000\\ =\$25,600\end{array}$

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.

$\begin{array}{c}\text{Total overtime cost}=\text{Overtime of all the months}\\ =\$0+\$0+\$0+\$25,600+\$22,400+\$0\\ =\$48,000\end{array}$

Hence, the total overtime cost is 48,000.

Calculate the subcontract cost for the month of May:

Subcontract cost per unit is given as $20 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.

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

Calculate the subcontract cost for the month of June:

Subcontract cost per unit is given as $20 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.

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

Calculate the subcontract cost for the month of July:

Subcontract cost per unit is given as $20 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.

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

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 May:

It is calculated by average balance inventory cost and the average inventory units. Hence, the inventory cost is $500.

$\begin{array}{c}\text{Inventory cost}=\text{Inventory cost per unit}\times \text{Average inventory}\\ =\$1\times 500\\ =\$500\end{array}$

Calculate the inventory cost for the month of June:

It is calculated by average balance inventory cost and the average inventory units. Hence, the inventory cost is $1,100.

$\begin{array}{c}\text{Inventory cost}=\text{Inventory cost per unit}\times \text{Average inventory}\\ =\$1\times 1,100\\ =\$1,100\end{array}$

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 $900.

$\begin{array}{c}\text{Inventory cost}=\text{Inventory cost per unit}\times \text{Average inventory}\\ =\$1\times 900\\ =\$900\end{array}$

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.

$\begin{array}{c}\text{Total inventory cost}=\text{Inventory cost of all the months}\\ =\$500+\$1,100+\$900+\$300+\$0+\$0\\ =\$2,800\end{array}$

Hence, the total inventory cost is $2,800.

Calculate the total cost of the plan:

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

$\begin{array}{c}\text{Total cost of the plan}=\left(\begin{array}{l}\text{Total regular time cost}+\text{Total overtime cost}+\\ \text{Total subcontract cost}+\text{Total inventory cost}+\\ \text{Total backorder cost}\end{array}\right)\\ =\$300,000+\$0+\$48,000+\$2,800+\$0\\ =\$350,800\end{array}$

Hence, the total cost of the plan is $350,800.

Summary Introduction

To determine: The total cost using level strategy of aggregate planning.

Introduction: Level production strategy is a production strategy used to produce at a constant rate. This strategy keeps constant level of workforce and backlog of demand.

Answer to Problem 8P

The total cost of the aggregate plan is $356,200.

Explanation of Solution

Given information:

Regular production cost is $10, overtime production cost is $16, subcontracting cost is $20, holding cost is $1, regular capacity is 5,000 units, and beginning inventory is given as 0 units. Maximum subcontract capacity is 500 units and maximum overtime capacity is 500 units. In addition to this forecast for 6 months is given as follows:

Month	July	June	July	August	September	October	Total
Forecast	4,000	4,800	5,600	7,200	6,400	5,000	33,000

Determine the total cost of the plan:

It is given that regular productions should be used. No backlogs are allowed. Supplements can be satisfied using overtime.

Supporting explanation:

Calculate the difference for the month of May:

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 1,500 units.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overitme}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(5,000+500+0\right)-4,000\\ =1,500\end{array}$

Calculate the difference for the month of June:

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 700 units.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overitme}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(5,000+500+0\right)-4,800\\ =700\end{array}$

Calculate the difference for the month of 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 -100 units.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overitme}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(5,000+500+0\right)-5,600\\ =-100\end{array}$

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 May:

Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 1,500 units.

$\begin{array}{c}\text{Ending inventory}=\text{Beginning inventory}+\text{Difference between output and forecast}\\ =0+1,500\\ =1,500\end{array}$

Ending inventory for the month of June:

Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 2,200 units.

$\begin{array}{c}\text{Ending inventory}=\text{Beginning inventory}+\text{Difference between output and forecast}\\ =1,500+700\\ =2,200\end{array}$

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 2,100 units.

$\begin{array}{c}\text{Ending inventory}=\text{Beginning inventory}+\text{Difference between output and forecast}\\ =2,200-100\\ =2,100\end{array}$

Note: The calculation repeats for all the months.

Average inventory for the month of May:

It is calculated by taking an average of beginning inventory and ending inventory. Hence, the average inventory is 750 units.

$\begin{array}{c}\text{Average inventory}=\frac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\ =\frac{0+1,500}{2}\\ =750\end{array}$

Average inventory for the month of June:

It is calculated by taking an average of beginning inventory and ending inventory. Hence, the average inventory is 1,850 units.

$\begin{array}{c}\text{Average inventory}=\frac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\ =\frac{1,500+2,200}{2}\\ =1,850\end{array}$

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 2,150 units.

$\begin{array}{c}\text{Average inventory}=\frac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\ =\frac{2,200+2,100}{2}\\ =2,150\end{array}$

Note: The calculation repeats for all the months.

Calculate the regular time cost for the month of May:

Regular time cost per unit is given as $10 and regular time unit is given as 5,000. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $50,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$10\times 5,000\\ =\$50,000\end{array}$

Calculate the regular time cost for the month of June:

Regular time cost per unit is given as $10 and regular time unit is given as 5,000. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $50,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$10\times 5,000\\ =\$50,000\end{array}$

Calculate the regular time cost for the month of July:

Regular time cost per unit is given as $10 and regular time unit is given as 5,000. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $50,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$10\times 5,000\\ =\$50,000\end{array}$

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.

$\begin{array}{c}\text{Total regular time cost}=\text{Regular time of all the months}\\ =\$50,000+\$50,000+\$50,000+\$50,000+\$50,000+\$50,000\\ =\$300,000\end{array}$

Hence, the total regular time cost is $300,000.

Calculate the overtime cost for the month of May:

Overtime cost per unit is given as $16 and overtime unit is given as 500. Overtime cost is calculated by multiplying overtime unit and overtime cost per unit. Hence, the overtime cost is $8,000.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$16\times 500\\ =\$8,000\end{array}$

Calculate the overtime cost for the month of June:

Overtime cost per unit is given as $16 and overtime unit is given as 500. Overtime cost is calculated by multiplying overtime unit and overtime cost per unit. Hence, the overtime cost is $8,000.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$16\times 500\\ =\$8,000\end{array}$

Calculate the overtime cost for the month of July:

Overtime cost per unit is given as $16 and overtime unit is given as 500. Overtime cost is calculated by multiplying overtime unit and overtime cost per unit. Hence, the overtime cost is $8,000.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$16\times 500\\ =\$8,000\end{array}$

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.

$\begin{array}{c}\text{Total overtime cost}=\text{Overtime of all the months}\\ =\$8,000+\$8,000+\$8,000+\$8,000+\$8,000\\ =\$40,000\end{array}$

Hence, the total overtime cost is 40,000.

Calculate the subcontract cost for the month of May:

Subcontract cost per unit is given as $20 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.

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

Calculate the subcontract cost for the month of June:

Subcontract cost per unit is given as $20 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.

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

Calculate the subcontract cost for the month of July:

Subcontract cost per unit is given as $20 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.

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

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.

$\begin{array}{c}\text{Total subcontract cost}=\text{Subcontract of all the months}\\ =\$0+\$0+\$0+\$0+\$10,000+\$0\\ =\$10,000\end{array}$

Hence, the total subcontract cost is $10,000.

Calculate the inventory cost for the month of May:

It is calculated by average balance inventory cost and the average inventory units. Hence, the inventory cost is $750.

$\begin{array}{c}\text{Inventory cost}=\text{Inventory cost per unit}\times \text{Average inventory}\\ =\$1\times 750\\ =\$750\end{array}$

Calculate the inventory cost for the month of June:

It is calculated by average balance inventory cost and the average inventory units. Hence, the inventory cost is $1,850.

$\begin{array}{c}\text{Inventory cost}=\text{Inventory cost per unit}\times \text{Average inventory}\\ =\$1\times 1,850\\ =\$1,850\end{array}$

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 $2,150.

$\begin{array}{c}\text{Inventory cost}=\text{Inventory cost per unit}\times \text{Average inventory}\\ =\$1\times 2,150\\ =\$2,150\end{array}$

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.

$\begin{array}{c}\text{Total inventory cost}=\text{Inventory cost of all the months}\\ =\$750+\$1,850+\$2,150+\$1,250+\$200+\$0\\ =\$6,200\end{array}$

Hence, the total inventory cost is $6,200.

Calculate the total cost of the plan:

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

$\begin{array}{c}\text{Total cost of the plan}=\left(\begin{array}{l}\text{Total regular time cost}+\text{Total overtime cost}+\\ \text{Total subcontract cost}+\text{Total inventory cost}+\\ \text{Total backorder cost}\end{array}\right)\\ =\$300,000+\$40,000+\$10,000+\$0+\$6,200\\ =\$356,200\end{array}$

Hence, the total cost of the plan is $356,200.

Summary Introduction

To determine: The total cost using aggregate planning.

Introduction: Level production strategy is a production strategy used to produce at a constant rate. This strategy keeps constant level of workforce and backlog of demand.

Answer to Problem 8P

The total cost of the aggregate plan is $353,700.

Explanation of Solution

Given information:

Regular production cost is $10, overtime production cost is $16, subcontracting cost is $20, holding cost is $1, regular capacity is 5,000 units, overtime capacity is 750 units, and beginning inventory is given as 0 units. In addition to this forecast for 6 months is given as follows:

Month	July	June	July	August	September	October	Total
Forecast	4,000	4,800	5,600	7,200	6,400	5,000	33,000

Determine the total cost of the plan:

It is given that regular productions should be used. No backlogs are allowed. Supplements can be satisfied using overtime.

Supporting explanation:

Calculate the difference for the month of May:

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 1,000 units.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overitme}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(5,000+0+0\right)-4,000\\ =1,000\end{array}$

Calculate the difference for the month of June:

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 950 units.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overitme}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(5,000+750+0\right)-4,800\\ =950\end{array}$

Calculate the difference for the month of 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 150 units.

$\begin{array}{c}\text{Difference}=\text{Output}-\text{Forecast}\\ \text{=}\left(\text{Regular}+\text{Overitme}+\text{Subcontract}\right)-\text{Forecast}\\ \text{=}\left(5,000+750+0\right)-5,600\\ =150\end{array}$

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 May:

Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 1,000 units.

$\begin{array}{c}\text{Ending inventory}=\text{Beginning inventory}+\text{Difference between output and forecast}\\ =0+1,000\\ =1,000\end{array}$

Ending inventory for the month of June:

Ending inventory can be determined by adding the beginning inventory and difference between output and forecast. Hence, the ending inventory is 1,950 units.

$\begin{array}{c}\text{Ending inventory}=\text{Beginning inventory}+\text{Difference between output and forecast}\\ =1,000+950\\ =1,950\end{array}$

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 2,100 units.

$\begin{array}{c}\text{Ending inventory}=\text{Beginning inventory}+\text{Difference between output and forecast}\\ =1,950+150\\ =2,100\end{array}$

Note: The calculation repeats for all the months.

Average inventory for the month of May:

It is calculated by taking an average of beginning inventory and ending inventory. Hence, the average inventory is 500 units.

$\begin{array}{c}\text{Average inventory}=\frac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\ =\frac{0+1,000}{2}\\ =500\end{array}$

Average inventory for the month of June:

It is calculated by taking an average of beginning inventory and ending inventory. Hence, the average inventory is 1,475 units.

$\begin{array}{c}\text{Average inventory}=\frac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\ =\frac{1,000+1,950}{2}\\ =1,475\end{array}$

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 2,025 units.

$\begin{array}{c}\text{Average inventory}=\frac{\text{Beginning inventory}+\text{Ending inventory}}{2}\\ =\frac{1,950+2,100}{2}\\ =2,025\end{array}$

Note: The calculation repeats for all the months.

Calculate the regular time cost for the month of May:

Regular time cost per unit is given as $10 and regular time unit is given as 5,000. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $50,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$10\times 5,000\\ =\$50,000\end{array}$

Calculate the regular time cost for the month of June:

Regular time cost per unit is given as $10 and regular time unit is given as 5,000. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $50,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$10\times 5,000\\ =\$50,000\end{array}$

Calculate the regular time cost for the month of July:

Regular time cost per unit is given as $10 and regular time unit is given as 5,000. Regular time cost is calculated by multiplying regular time unit and regular time cost per unit. Hence, the regular time cost is $50,000.

$\begin{array}{c}\text{Regular time cost}=\text{Regular time cost per unit}\times \text{Regular time units}\\ =\$10\times 5,000\\ =\$50,000\end{array}$

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.

$\begin{array}{c}\text{Total regular time cost}=\text{Regular time of all the months}\\ =\$50,000+\$50,000+\$50,000+\$50,000+\$50,000+\$50,000\\ =\$300,000\end{array}$

Hence, the total regular time cost is $300,000.

Calculate the overtime cost for the month of May:

Overtime cost per unit is given as $16 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.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$16\times 0\\ =\$0\end{array}$

Calculate the overtime cost for the month of June:

Overtime cost per unit is given as $16 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.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$16\times 0\\ =\$0\end{array}$

Calculate the overtime cost for the month of July:

Overtime cost per unit is given as $16 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.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$16\times 0\\ =\$0\end{array}$

Calculate the overtime cost for the month of August:

Overtime cost per unit is given as $16 and overtime unit is given as 1,600. Overtime cost is calculated by multiplying overtime unit and overtime cost per unit. Hence, the overtime cost is $25,600.

$\begin{array}{c}\text{Overtime cost}=\text{Overtime cost per unit}\times \text{Overtime units}\\ =\$16\times 16,000\\ =\$25,600\end{array}$

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.

$\begin{array}{c}\text{Total overtime cost}=\text{Overtime of all the months}\\ =\$0+\$0+\$0+\$25,600+\$22,400+\$0\\ =\$48,000\end{array}$

Hence, the total overtime cost is 48,000.

Calculate the subcontract cost for the month of May:

Subcontract cost per unit is given as $20 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.

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

Calculate the subcontract cost for the month of June:

Subcontract cost per unit is given as $20 and subcontract unit is given as 750. Subcontract cost is calculated by multiplying subcontract unit and subcontract cost per unit. Hence, the subcontract cost is $12,000.

$\begin{array}{c}\text{Subcontract cost}=\text{Subcontract cost per unit}\times \text{Subcontract units}\\ =\$20\times 750\\ =\$12,000\end{array}$

Calculate the subcontract cost for the month of July:

Subcontract cost per unit is given as $20 and subcontract unit is given as 750. Subcontract cost is calculated by multiplying subcontract unit and subcontract cost per unit. Hence, the subcontract cost is $12,000.

$\begin{array}{c}\text{Subcontract cost}=\text{Subcontract cost per unit}\times \text{Subcontract units}\\ =\$20\times 750\\ =\$12,000\end{array}$

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.

$\begin{array}{c}\text{Total subcontract cost}=\text{Subcontract of all the months}\\ =\$0+\$12,000+\$12,000+\$12,000+\$12,000+\$0\\ =\$48,000\end{array}$

Hence, the total subcontract cost is $48,000.

Calculate the inventory cost for the month of May:

It is calculated by average balance inventory cost and the average inventory units. Hence, the inventory cost is $500.

$\begin{array}{c}\text{Inventory cost}=\text{Inventory cost per unit}\times \text{Average inventory}\\ =\$1\times 500\\ =\$500\end{array}$

Calculate the inventory cost for the month of June:

It is calculated by average balance inventory cost and the average inventory units. Hence, the inventory cost is $1,475.

$\begin{array}{c}\text{Inventory cost}=\text{Inventory cost per unit}\times \text{Average inventory}\\ =\$1\times 1,475\\ =\$1,475\end{array}$

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 $2,025.

$\begin{array}{c}\text{Inventory cost}=\text{Inventory cost per unit}\times \text{Average inventory}\\ =\$1\times 2,025\\ =\$2,025\end{array}$

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.

$\begin{array}{c}\text{Total inventory cost}=\text{Inventory cost of all the months}\\ =\$500+\$1,475+\$2,025+\$1,375+\$325+\$0\\ =\$5,700\end{array}$

Hence, the total inventory cost is $5,700.

Calculate the total cost of the plan:

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

$\begin{array}{c}\text{Total cost of the plan}=\left(\begin{array}{l}\text{Total regular time cost}+\text{Total overtime cost}+\\ \text{Total subcontract cost}+\text{Total inventory cost}+\\ \text{Total backorder cost}\end{array}\right)\\ =\$300,000+\$0+\$48,000+\$5,700+\$0\\ =\$353,700\end{array}$

Hence, the total cost of the plan is $350,800.

Conclusion

Conclusion: Plan from Part (a) should be selected, as it has the lowest cost ($350,800).