2-A manufacturer of plastics is planning to blend a new product from four chemic

Question

2-A manufacturer of plastics is planning to blend a new product from four chemical compounds. These compounds are mainly composed of three elements: A, B, and C. The composition and unit cost of these chemicals are shown in the following table: CHEMICAL COMPOUND Percentage A Percentage B Percentage C Cost/kilogram 35 20 40 20 35 35 25 20 4 25 40 30 65 30 The new product consists of 25 percent element A, at least 35 percent element B, and at least 20 percent element C. Owing to side effects of compounds 1 and 2, they must not exceed 25 percent and 30 percent, respectively, of the content of the new product. A) Formulate he problem of finding the least costly way of blending as a linear program. B) Calculate the optimum value for objective function and optimal value for each one of the decision variables used in your model, by using M.S EXCEL solver.

Explanation / Answer

(A)

Let there be 100 kg of final product to be made
Let P1, P2, P3, and P4 be the KG of Compound 1, 2, 3, 4 respectively mixed in the final product

Objective Function: min. Z = Total Cost = 20P1 + 30P2 + 20P3 + 15P4

Subject to,

P1 + P2 + P3 + P4 = 100

0.35P1 + 0.15P2 + 0.35P3 + 0.25P4 = 25
0.20P1 + 0.65P2 + 0.35P3 + 0.40P4 35
0.40P1 + 0.15P2 + 0.25P3 + 0.30P4 20

P1 25
P2 30

P1, P2, P3, P4 0

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(B)

From the solution, it is clear the only including compound 4 (100%) is optimal to give the minimum cost.

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