Reference no: EM132323553
Operation Research Assignment - Solve the following problems using LP Modeling and the Simplex Algorithm.
Problem 1: Reddy Mikks produces both interior and exterior paints from two raw materials, M1 and M2. The following table provides the basic data of the problem:
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Tons of raw material per ton of
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Maximum daily availability (tons)
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Exterior paint
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Interior paint
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Raw material, M1
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6
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4
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24
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Raw material, M2
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1
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2
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6
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Profit per ton ($1000)
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5
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4
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A market survey indicates that the daily demand for interior paint cannot exceed that of exterior paint by more than 1 ton. Also, the maximum daily demand of interior paint is 2 tons.
Reddy Mikks wants to determine the optimum (best) product mix of interior and exterior paints that maximizes the total daily profit.
Problem 2: A firm manufactures two types of products A and B and sells them at a profit of $2 on type A and $3 on type B. Each product is processed on two machines G and H. Type A requires one minute of processing time on G and two minutes on H; type B requires one minute on G and one minute on H. The machine G is available for not more than 6 hour 40 minutes while machine H is available for not more than 10 hours during any working day. Formulate the problem as a linear programming problem and determine the optimum product mix of types A and B products.
Problem 3: A company produces two types of hats. Each hat of the first type requires twice as much labor time as the second type. The company can produce a total of 500 hats a day. The market limits daily sales of the first and second type to 150 and 250 hats respectively. Assuming that the profits per hat are $8 for type A and $5 for type B, formulate the problem as a linear programming model in order to determine the number of hats to be produced of each type so as to maximize the profit.
Problem 4: The manufacturer of patent medicines is proposed to prepare a production plan for medicines A and B. There are sufficient ingredients available to make 20,000 bottles of mdicine A and 40,000 bottles of medicine B, but there are only 45,000 bottles into which either of the medicines can be filled. Further, it takes three hours to prepare enough material to fill 1000 bottles of medicine A and one hour to prepare enough material to fill 1000 bottles of medicine B and there are 66 hours available for this operation. The profit is $8 per bottle for medicine A and $7 per bottle for medicine B.
1. Formulate this problem as L.P.P.
2. How the manufacturer schedule his production in order to maximize profit.
Problem 5: A toy company manufactures two types of doll, a basic version - doll A and a deluxe version - doll B. Each doll of type B takes twice as long to produce as one of type A, and the company would have time to make a maximum of 2000 per day. The supply of plastic is sufficient to produce 1500 dolls per day (both A and B combined). The deluxe version requires a fancy dress of which there are only 600 per day available. If the company makes a profit of $3 and $5 per doll, respectively on doll A and B, then how many of each doll should be produced per day in order to maximize the total profit. Formulate this problem in order to determine the number of dolls to be produced of each type so as to maximize the profit.