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)
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