Problem:
Smithton, Inc. produces four types of computer chips. Two of these (W and X) are sold by the business. The others (Y and Z) are incorporated, as components, into another of the company's products. Computer chips Y and Z are not incorporated into either computer chip W or X. The four types of computer chips have the following costings (per unit):
W X Y Z
Variable materials 100 90 80 92
Variable labour 50 30 45 57
Other variable costs 34 10 12 17
Fixed costs 25 18 34 13
Total cost per unit 209 148 171 179
Selling price per unit 250 220
An outside supplier is willing and able to supply unlimited quantities of products Y and Z to the business at a cost of 209 pounds per unit of computer chip Y and 196 pounds per unit of computer chip Z.
Smithton, Inc. has estimated the demand for its computer chips for the upcoming year. For chips W and X, the following is the market demand; for chips Y and Z, the following represents demand from estimated production requirements:
Units
W 6,500
X 5,500
Y 3,700
Z 3,400
Also, production of the computer chips is completed with a specialised machine. Each chip requires the following time:
Hours per unit
W 0.6
X 0.5
Y 0.6
Z 0.2
The machine is expected to be available for a maximum of 6,000 hours. No other shortages of any other production factor are expected.
Student tasks:
1. Complete the necessary calculations in order to determine which products the business should plan to make next year. You will need to state your suggestions and support them with the calculations and assumptions presented.
2. Propose and explain other ways that could help to solve the problem of the shortage of special machine time.