Froggatt Enterprises,a premier educational products company, experiences ups and downs in demand each year corresponding to major school holidays. The company maintains a steady workforce and uses overtime, inventory, and subcontracting to absorb fluctuations in demand. Expected demand, available capacities, and costs for the next four quarters are given below. There is no beginning inventory. Design a production plan that will satisfy demand at minimum cost. Period Demand Regular Capacity Overtime Capacity Subcontracting Capacity
1 600 1000 500 500
2 2100 1000 500 500
3 800 1000 500 500
4 1800 1000 500 500

Regular production cost per unit $8
Overtime production cost per unit $10
Subcontracting cost per unit $12
Inventory holding cost per unit per period $1

Answer is explained in the explanation section below.

Explanation:

Note: As this question contains tables, here I cannot insert table properly, so I have done it on excel spreadsheet and it is attached in the attachment below.  Please refer to the attachment below for the minimum cost production plan.

Please refer to Attachment.  

Priority should be given in the order mentioned below.

1. Maintain maximum capacity output even though demand is lower for the period because demand for the next period is higher and inventory holding costs are only $1 per unit per period.

2. Over time output for remaining demand, including demand for the following year, since it is less costly than subcontract production and inventory keeping costs are just $1 per unit per period.

3. There is no obligation for output to be subcontracted.

A (5,250) sold at split-off

B 22,625 continue

C (10,400) sold at split-off

Explanation:

Result for further processing:

quantity ( further process price - raw price) less further processing cost

Product A

13,800 pounds x (29.5 - 24) - 81,150 = (5,250)

Product B

21,500 pounds (24.50 - 18) - 117,125 = 22,625

Product C

5,000 gallon ( 38.5 - 30) - 52,900 = (10,400)

We must understand that the join processing cost are already incurred (sunk) therefore, not relevant. We hould check if the further process increases or not the gross profit.

As B is the only which increase the gross profit we continue the processing. THe other product based on our cost structure are not viable