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practice_5 - Practice#5 Linear Programming BUAD311...

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Practice #5 Linear Programming BUAD311 – Operations Management Spring 2011 1. The company produces three products, X, Y, and Z. Each unit of product X yields a profit of $12, Y $18, and Z $15. To produce the products we need three machines 1, 2, and 3 and machine hour requirements for the three products are: X Y Z machine1 5 4 3 machine2 4 10 4 machine3 2 2 4 The above table can be found in the spreadsheet file practice_3.xls. Machine1 has 160 hours available to produce this period, machine2 has 288 hours, and machine3 has 200 hours. There is additional requirement from the upper management that we can’t produce more than 16 units of product Y. a) Identify the decision variable(s). State in words. For example, do not answer “X and Y,” but “#units of product X we produce,” etc. b) Formulate and solve the following LP using Excel Solver. What is the optimal objective value? What are the corresponding decision variables?
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2. The B&D Toy company produces toys in 3 factories all over the world. The toys are delivered to 4 regional warehouses in the USA Boston, Chicago, Pittsburgh, and Los Angeles. The B&D plan calls for the following number of toys to be delivered at each location: Boston: 70,000 Chicago: 70,000 Pittsburgh: 60,000 Los Angeles: 80,000 The capacity of each plant is as follows: Jerusalem 100,000 Bombay 220,000 Ankara 150,000 The transportation cost B&D pays per unit depends on where they were produced and where they were stored. The following table gives the accounting department’s estimates of these costs Shipped to Produced at Boston Chicago Pittsburgh Los Angeles Jerusalem 10 15 10 13 Bombay 20 10 21 10 Ankara 14 18 19 20 The above table can be found in the spreadsheet file practice_3.xls. The company can’t ship from Jerusalem to Pittsburgh more than 50000 units. Chicago will not accept toys made in Bombay. a) Identify the decision variable(s). State in words. For example, do not answer “X and Y,” but “#units of product X we produce,” etc. b) Formulate and solve the following LP using Excel Solver. What is the optimal objective value? What are the corresponding decision variables?
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3. Finco Investment Corporation must determine an investment strategy for the firm for the next 3 years. At present (time 0), $100,000 is available for investment.
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