(1) Consider a small production system for manufacturing two products, X and Y as shown below. Manufacturing X requires two raw materials (RM 1 and 2). Manufacturing Y also requires two raw materials (RM 2 and 3). In addition, Y uses a purchased component that costs $10 per unit. Four work centers (A, B, C, and D) are used to manufacture the products. Each has 7,200 minutes (120 hours; 3-eight hour shifts) available each week. Operating expenses for the week, including everything except materials costs, is $12,000. X Y Demand per week 300 units 150 units Selling price $180/unit $200/unit Raw material costs (per unit) RM 1 $40 RM 2 $40 $40 RM 3 $40 Purchased parts $10 Time available on each work center is 7,200 minutes.

(a) What is the maximum potential profit of the production system?

(b) Find the bottleneck work center. Show why it is a constraint.

(c) What is the maximum feasible amount of profit subject to the constraint?

(d) The manager plans to purchase a new technology at $750,000 to reduce the processing time on both RM 2 and RM 3 at the bottleneck workstation by half. What would you say about his plan? Discuss.