The company manufactures and sells two products P and Q. The selling price of product P is $90 per unit and the market demand (which is accurately known to the last unit) is 100 units per week. The selling price of product Q is $100 each and the market demand is 50 units per week. Three raw materials and one purchased part are used to make the two products P and Q. One unit of each of each raw materials 1 and 2 combined with one purchased part constitutes the chain for product P. One unit of each raw materials 2 and 3 constitutes the chain for product Q. For product P, raw material 1 is processed at machines (resource) A, C, & D but not at machine B. Raw material 2 is processed at machines B, C, and D but not on machine A. One unit of raw materials 1 and 2 along with one unit of purchased part are combined at machine D to produce one unit of product P. For product Q, raw material 2 is processed at sections B, C, & D but not at section A. Raw material 3 is processed at sections A, B, & D but not at section C. One unit each of raw materials 2 and 3 are combined in section D to produce one unit of product Q.

The Figure below shows the routing and time required for each operation and the unit costs of the raw materials and purchased part. P $90/U 100 U/WK $100/U 50 U/WK D 15min D 5 Min C 10 min C 5 min B 15 min A 15 min B 15 min A 10 min RM1 $20/u 20/U RM2$ 20/u 20/U RM3$ 20/u 20/U Part $5/u $5 Q The operating expense for the whole process is $6,000 per week. Each resource is available for 60 minutes per hour, 8 hours per day, and 5 days per week (or 2,400 minutes per week). There is never any waiting: i. e., when one step finishes, the next step is immediately ready.

With the information given thus far, please answer the following questions:

1. Is market a constraint? Why or why not?

2. Which resource is a constraint? Why?

3. What are the optimal quantities of Product P and Q to be produced?

4. Now, an engineer X in the company, through the suggestion box, suggests that by making an investment of $5,000, he can decrease the time required on machine A by eight minutes per unit. Should this proposal be accepted? Why or why not?

5. Another engineer Y in the company, through the suggestion box, suggests that by making an investment of $5,000, she can decrease the processing time on machine B by 2.5 minutes. However, this will increase the time on machine C by 2 minutes as well (as her proposal is to redesign the processing in such a way that some of the work done on machine B will shift to machine C). Would you accept this proposal? Why or why not?