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1. The Surest Concrete Company produces concrete in a continuous process. Two in

ID: 454892 • Letter: 1

Question

1. The Surest Concrete Company produces concrete in a continuous process. Two ingredients in the concrete are sand which Surest purchases for $6 per ton and, and gravel, which costs $8 per ton. Sand and gravel together must make up exactly seventy-five percent of the weight of the concrete. Furthermore, no more than 40 percent of the concrete can be sand and at least 30 percent of the concrete must be gravel. Each day 2,000 tons of concrete are produced. Formulate as a linear programming problem.

Explanation / Answer

Let X1 be tons of sand purchased

X2 be tons of gravel purchased

The objective function is

MIN Z = 6X + 8Y

Subject to:

X1 + X2 = 1500 (75% * 2,000 = 1500) Sand and gravel together must make up exactly seventy-five percent of the weight of the concrete.

X1 <= 800 (40% * 2000) No more than 40 percent of the concrete can be sand

X2 >= 600 (30 % * 2000) Atleast 30 percent of the concrete must be gravel

X1, X2 >=0 (non zero constraints)