A company manufactures two products. For $1.00 worth of product A, the company s

Question

A company manufactures two products. For $1.00 worth of product A, the company

spends $0.50 on materials, $0.20 on labor, and $0.15 on overhead. For $1.00 worth of product B, the company spends $0.45 on materials, $0.20 on labor, and $0.15 on overhead. Let

A =

B=

Then a and b represent the "costs per dollar of income" for the two products. Suppose the company manufactures x1 dollars worth of product A and x2 dollars worth of product B and that its total costs for materials are $140, its total costs for labor are $60, and its total costs for overhead are $45. Determine x1 and x2, the dollars worth of each product produced. Include a vector equation as part of your solution.

Explanation / Answer

Suppose the company manufactures x1 dollars worth of product A and x2 dollars worth of product B

Materials : 0.5x1 + 0.45x2 = 140 -----(1)

Labor : 0.2x1 + 0.2x2 = 60 -----(2)

Overhead : 0.15x1 +0.15x2 = 45 ----(3)

Equation 2 and 3 are same

So, solve for x1 and x2 using

0.5x1 + 0.45x2 = 140

0.15x1 +0.15x2 = 45

On solveing we get : x1 = $100 ; x2 = $200

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