SOM 464HOMEWORK PROBLEMS R. Gunther

Fall 2010Set #1

Product Mix - Resource Allocation

Master Production Scheduling (MPS)

1.The Suds Beer Company produces two products. "Hightime" contributes $9/unit to profit and overhead; "Lushline," a stronger brew, contributes $7/unit. There are four processes in the plant. The time required for each product at each process is given below. The capacity, stated in minutes per day is also given. What is the optimum product mix? Formulate and solve using POM/QM for Windows on the computer.

Process

1 2 3 4

Requirement in Min/Unit

Hightime 5 6 7 0

Lushline 8 0 4 9

560 420 560 450 capacity in min.

2.The businessperson, Cindy Light, publishes two magazines, Paygirl (for men) and Payboy (for women). Monthly sales average about 6,000 and 4,500 issues respectively for the publications. Paygirls contribute $.60 per issue to net profits; Payboys add about $.50 per issue. No left over magazines are desirable.

Each Paygirl requires two minutes of actual machine and labor time to produce. Payboys only require one minute. There are 10,000 total minutes per month of time available. Inventory storage space imposes another limitation. 48,000 cubic inches are available and each magazine uses up about 8.

Determine monthly production for each magazine. Formulate and solve using POM/QM for Windows on the computer.

3.The Pyrotec Company produces three electrical products - clocks, radios, and toasters. These products have the following resource requirements.

Resource Requirements

Product Cost/Unit Labor Hours/Unit

Clock$ 7 2

Radio 10 3

Toaster 5 2

The manufacturer has a daily production budget of $2,000 and a maximum of 660 hours of labor. Maximum daily customer demand is for 200 clocks, 300 radios, and 150 toasters. Selling prices are $15 for a clock, $20 for a radio, and $12 for a toaster. The company desires to know the optimal product mix that will maximize profit. Formulate a linear programming model for this problem. Solve using POM/QM for Windows on the computer.

  1. The Politico Fertilizer Co. produces two brands, Republican and Democratic. Republican fertilizer sells for $2 per ton and the Democratic brand goes for $1 per ton. Weekly demand is 1 ton for the Republican brand and 2 tons for the Democratic variety. Storage space limits the firm to 6 square yards; the Democratic brand uses up about 2 square yards per ton and the Republican variety uses up about 3 square yards per ton. Determine weekly production for the two products. Formulate and solve using POM/QM for Windows on the computer.
  1. The Neptune Fish Market in Denver advertises fresh seafood. Its three main items are shrimp, lobster, and crabs, which it must fly in to Denver from Florida, Maine, and Baltimore, respectively. The maximum amount of seafood that can be flown in per day is 200 pounds. The shipping costs per pound for shrimp, lobster and crabs are $3, $6, and $4, respectively, and the market has $500 available for shipping each day. Once the seafood is received by the market it must be cleaned and packaged. A pound of shrimp requires 15 minutes of preparation, a pound of lobster 5 minutes, and a pound of crab 4 minutes. The market has 8 hours available daily to prepare the seafood. A pound of shrimp earns the market $10 in contribution, a pound of lobster earns $12, and a pound of crab earns $9. The market manager wishes to know how many pounds of each time of seafood to order each day in order to maximize contribution. Formulate and solve using POM/QM for Windows.
  1. Management at the Quality Mix Candy Company, which only manufactures all-day suckers, has decided to produce three flavors, tangy tangerine (T), luscious lemon (L), and groovy grape (G). Sales goals for April require the production of at least 95,000 suckers. The workforce is set at 10 for the month. Each worker can produce up to 10,000 lemon, 9,500 grape, or 9,000 tangerine suckers, as well as linear combinations of the three. The demand for April is 25,000 for T, 30,000 for L, and 45,000 for G. Since candy does not keep well for long periods, the company wishes to sell everything it produces. Production of one unit of T, L, and G contributes $0.50, $0.25, and $0.40 to profits, respectively. What is production for April? Formulate and solve using POM/QM for Windows.
  1. Try problem 3.1 (page 68) in the text.
  1. Try problem 3.4 (page 70) in the text.
  1. Try problem 3.6 (page 71) in the text.
  1. Try problem 3.11 (page 73) in the text.