Bill Kemp is an industrial engineer in charge of production planning at Keystone Products. The company assembles three products from components purchased from outside suppliers. Production might be limited by market demand, the assembly capacity at several departments, and the availability of certain critical components.

Market demand during the planning period is limited to 400 units/week of product A, 500 units/week of product B, and 300 units/week of product C. The company has firm contracts with vendors to supply at least 100 units/week of product A, 150 units/week of product B, and 100 units/week of product C. The company must produce enough units to meet pre-existing contract, but should not produce more than the units demanded for any product. Profit contribution has been determined to be $150/unit on product A, $100/unit on product B, and $200/unit on product C.

Product A requires 5 minutes of assembly time in Shop 1, 4 minutes of assembly time in Shop 2, and 2 minutes of assembly time in Shop 3. Product B requires 4 minutes in Shop 1, 2 minutes in Shop 2, and 6 minutes in Shop 4. Product C requires 3 minutes in Shop 1, 4 minutes in Shop 3, and 10 minutes in Shop 5. The shops work 5 days per week. Shop 1 is able to operate 12 hours per day, Shop 2 is limited to 14 hours per day, Shop 3 is limited to 8 hours per day, Shop 4 is limited to 12 hours per day, and Shop 5 is limited to 10 hours per day.

Product A uses a special microchip that is limited to 500 chips/week. We will call this Microchip X. Product B also uses Microchip X. Product B also uses Microchip Y, which is limited to 400 chips/week. Product C uses a third chip, Microchip Z, which is limited to 600 chips/week.

a.) How many units of each product should be scheduled for production each week, and what would be the weekly profit?

b.) What constraints are binding? That is, which constraints are at their limit?

c.) Should Kemp consider increasing capacity at any of the shops, and if so, which ones?

Answer rating: 100% (QA)

solution a 350 units of A 150 units of B and 300 unit... View the full answer