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

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

Algebraic formulation Decision Variables: X1 Qty of Sand tons X2 Qty of Gravel tons Objective function : Minimise cost :         Z = 6*X1 + 8*X2 subject to constraints : RHS 1*X1 + 1*X2 = 1500 (=75%*2000) 1*X1 + 0*X2 = 600 (=30%*2000) X1, X2 >= 0

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