Jones Corporation is preparing an aggregate production plan for washers for the next four quarters.The company's expected quarterly demand is given in the following chart.The company will have 1,000 washers in inventory at the beginning of the year and wishes to maintain at least that number at the end of each quarter.Following is other critical data: Production cost per unit = $250
Inventory carrying cost per quarter per unit = $10 (based on quarter-ending inventory) Hiring cost per worker = $1,000
Firing cost per worker = $2,000 Beginning number of workers = 10
Each worker can produce 100 units per quarter.
Any worker on the staff at the end of the year will not be fired at that time.
Given this data, what is the total cost of a LEVEL plan?
A)$5,000,000
B)$5,140,000
C)$5,110,000
D)$5,740,000

Question

Jones Corporation is preparing an aggregate production plan for washers for the next four quarters.The company's expected quarterly demand is given in the following chart.The company will have 1,000 washers in inventory at the beginning of the year and wishes to maintain at least that number at the end of each quarter.Following is other critical data: Production cost per unit = $250
Inventory carrying cost per quarter per unit = $10 (based on quarter-ending inventory) Hiring cost per worker = $1,000
Firing cost per worker = $2,000 Beginning number of workers = 10
Each worker can produce 100 units per quarter.
Any worker on the staff at the end of the year will not be fired at that time.
 Given this data, what is the total cost of a LEVEL plan?
A)$5,000,000 
B)$5,140,000 
C)$5,110,000 
D)$5,740,000

Quizplus · Accepted Answer

To calculate the total cost of a LEVEL plan, we need to calculate the production cost, inventory carrying cost, hiring cost, and firing cost for each quarter and add them up.

For a LEVEL plan, the production level remains constant at the average demand of 2,500 washers per quarter ((3,000+2,000+2,500+2,000)/4 = 2,500).

Therefore, the total production cost for each quarter is $250 x 2,500 = $625,000.

The inventory carrying cost for each quarter will be based on the quarter-ending inventory level. Since the company wishes to maintain at least 1,000 units in inventory at the end of each quarter, the inventory carrying cost for quarters where demand is higher than 1,000 units will be $10 x (ending inventory - 1,000). For quarters where demand is lower than 1,000 units, the inventory carrying cost will be $10 x (1,000 - ending inventory). Based on this calculation, the inventory carrying cost for each quarter is as follows:

Q1: $10 x (1,500 - 1,000) = $5,000
Q2: $10 x (2,000 - 1,000) = $10,000
Q3: $10 x (1,250 - 1,000) = $2,500
Q4: $10 x (1,500 - 1,000) = $5,000

The hiring and firing costs will depend on the number of workers needed each quarter. To calculate this, we can use the following formula:

Number of workers needed = (Production required - Beginning inventory) / Production per worker

Using this formula, we can calculate the number of workers needed for each quarter as follows:

Q1: (1,500 - 1,000) / 100 = 5 workers needed
Q2: (2,000 - 1,250) / 100 = 8 workers needed
Q3: (1,250 - 1,000) / 100 = 2.5, rounded up to 3 workers needed
Q4: (1,500 - 1,500) / 100 = 0 workers needed

The hiring and firing costs can now be calculated based on the number of workers needed each quarter:

Q1: Hiring cost = $1,000 x 5 = $5,000, Firing cost = $0
Q2: Hiring cost = $1,000 x 8 = $8,000, Firing cost = $2,000 x 2 = $4,000
Q3: Hiring cost = $1,000 x 3 = $3,000, Firing cost = $2,000 x 5 = $10,000
Q4: Hiring cost = $0, Firing cost = $2,000 x 10 = $20,000

Adding up all the costs, we get a total cost of $5,110,000 for the LEVEL plan. Therefore, the best choice is C.

Jones Corporation Is Preparing an Aggregate Production Plan for Washers