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# Some graphical LPP problems

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1. A clothier makes coats and slacks. the two resources are wool cloth and labor. The clothier has 150 square yards of wool and 200 hours of labor available. Each coat requires 3 square yards of wool and 10 hours of labor, whereas each pair of slacks requires 5 square yards of wool and 4 hours of labor. The profit for a cot is \$50, and the profit for slacks is \$40. The clothier wants to determine the number of coats and pairs of slacks to make so that profit will be maximized.

a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.

2. A company produces two products that are processes on two assembly lines. Assembly 1 has 100 available hours and assembly 2 has 42 available hours. Each product requires 10 hours of processing time on line 1, while on line 2 product requires 7 hours and product 2 requires 3 hours. The profit for product 1 is \$6 per unit and the profit for product 2 is \$4 per unit.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.

3. Universal Claims Processers processes insurance claims for large national insurance companies. Most claim processing is done by a large pool of computer operators, some of whom are permanent and some of whom are temporary. A permanent operator can process 16 claims per day, whereas a temporary operator can process 12 per day, and on average the company processes at least 450 claims each day. The company has 40 computer workstations. A permanent operator generates about 0.5 claims with errors each day, whereas a temporary operator averages about 1.4 defective claims per day. The company wants to limit claims with errors to 25 per day. A permanent operator is paid \$64 per day, and a temporary operator is paid \$42 per day. The company wants to determine the number of permanent and temporary operators to hire in order to minimize costs.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.

4. A manufacturing firm produces two products. Each product must undergo an assembly process and a finishing process. It is then transferred to the warehouse, which has space for only a limited number of items. The firm has 80 hours available for assembly and 112 hours for finishing and it can store a maximum of 10 units in the warehouse. Each unit of product 1 has a profit of \$30 and required 4 hours to assemble and 14 hours to finish. Each unit of product 2 has a profit of \$70 and requires 10 hours to assemble and 8 hours to finish. The firm wants to determine the quantity of each each product to produce in order to maximize profit.
a. Formulate a linear programming model for this problem.
a. Solve this model by using graphical analysis.

5. Janet Lopez is establishing an investment portfolio that will include stock and bond funds. She has \$720,000 to invest and she does not want the portfolio to include more than 65% stocks. The average annual return for the stock fund she plans to invest n is 18%, whereas the average annual return for the bond fund is 6%. She further estimates that the most she could lose in the next year in the stock fund is 22%, whereas the most she could lose in the bond fund is 5%. To reduce here risk she wants to limit her potential maximum losses to \$100,000.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.