S09-HW Soln-SupC

# S09-HW Soln-SupC - Supplement C Linear Programming Homework...

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Supplement C: Linear Programming Homework Problems Probett Problem #1: Solve these problems using simultaneous equations to determine the optimal values of the decision variables and the objective function. a. Maximize Z = 4x1 + 3x2 Subject to: Material: 6x1 + 4x2 <= 48 lb Labor: 4x1 + 8x2 <= 80 hr x1, x2 >= 0 b. Maximize Z = 6A + 3B Subject to: Material: 20A + 6B <= 600 lb Machinery: 25A + 20B <= 1000 hr A, B >= 0 Probett Problem #2: An appliance manufacturer produces two models of microwave ovens: H and W, Both models require fabrication and assembly work; each H uses four hours of fabrication and two hours of assembly, and each W uses two hours of fabrication and six hours of assembly. There are 600 fabrication hours available this week and 480 hours of assembly. Each H contributes \$40 to profits, and each W contributes \$30 to profits. What quantities of H and W will maximize profit? What is the maximum profit? Probett Problem #3: Solve each of these problems using Excel and obtain the optimal values of the decision variables and the objective function. Print the Excel “Answer Report”. a. Maximize Z = 4x1 + 2x2 + 5x3 Subject to: 1x1 + 2x2 + 1x3 <= 25 1x1 + 4x2 + 2x3 <= 40 3x1 + 3x2 + 1x3 <= 30 x1, x2, x3 >= 0 b. Max Z = 10x1 + 6x2 + 3x3 Subject to 1x1 + 1x2 + 2x3 <= 25 2x1 + 1x2 + 4x3 <= 40 1x1 + 2x2 + 3x3 <= 40 x1, x2, x3 >= 0 Probett Problem #4: The Erlanger Manufacturing Company makes two products. The profit estimates are \$25 for each unit of product 1 sold and \$30 for each unit of product 2 sold. The labor-hour 515dda97bdfc2ec15881744255b09f996c6a8c96.doc 1

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Supplement C: Linear Programming Homework Problems requirements for the products in the three production departments are shown in the following table. Product Department 1 2 A 1.50 3.00 B 2.00 1.00 C 0.25 0.25 The departments’ production supervisors estimate that the following number of labor- hours will be available during the next month: 450 hours in department A, 350 hours in department B, and 50 hours in department C. a. Develop a linear programming model to maximize profits. b. Find the optimal solution. How much of each product should be produced, and what is the projected profit? c. What are the scheduled production time and slack time in each department? Probett Problem #5: M&D Chemicals produces two products sold as raw materials to companies manufacturing bath soaps, laundry detergents, and other soap products. Based on an analysis of current inventory levels and potential demand for the coming month, M&D’s managers have specified that the total production of products 1 and 2 combined must be at least 350 gallons. Also, a major customer’s order for 125 gallons of product 1 must be satisfied. Product 1 requires two hours of processing time per gallon, and product 2 requires one hour; 600 hours of processing time are available in the coming month.
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