ewer urn - Open - 2. A manufacturer wishes to produce an alloy that is, by weigh

Question

ewer urn - Open - 2. A manufacturer wishes to produce an alloy that is, by weight, 30 % metal A and 70 % metal B. Five alloys are available at various prices as indicated below: Tha mix il-S. Alloy 1 2 3 4 5 % A 10 25 50 75 95 %B 90 75 50 25 5 Price/lb $ 5 $ 4 $ 3 $ 2 $ 1.50 The desired alloy will be produced by combining some of the other alloys. The manufacturer wishes to find the amounts of the various alloys needed and to determine the least expensive combination. Formulate this problem as a linear program. Box

Explanation / Answer

Let

x1 be the proportion of Alloy 1 used in the new alloy

x2 be the proportion of Alloy 2 used in the new alloy

x3 be the proportion of Alloy 3 used in the new alloy

x4 be the proportion of Alloy 4 used in the new alloy

x5 be the proportion of Alloy 5 used in the new alloy

So objective is to minimize Cost = 5x1 + 4x2 + 3x3 + 2x4 + 1.5x5

Subject to:

0.1x1 + 0.25x2 + 0.5x3 + 0.75x4 + 0.95x5 = 0.3

0.9x1 + 0.75x2 + 0.5x3 +0.25x4 + 0.05x5 = 0.7

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