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 $0.45 on materials, $0.20 on labor, $0.10 on overhead. For $1.00 worth of product b, the company spends $0.40 on materials, $0.20 on labor, and $0.15 on overhead.Let

a=0.45          And b=0.40

    0.20                      0.20

    0.10                      0.15

Then a and b represent the "cost 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 it's total costs for materials are $165, it's total costs for labor are $80, and it's total costs overhead are $55. Determine x1 and x2, the dollars worth of each product produced. Include a vector equation as part of your solution.

Explanation / Answer

Materials: a=0.45 And b=0.40

Labour: 0.20           0.20

Overhead: 0.10           0.15

x1 dollars of a, x2 dollars of b

=>   0.45x1 + 0.40 x2 = 165

and 0.20x1 + 0.20x2 = 80

=> 0.05 x1 = 5

=> x1 = 5/0.05 = 100

=> 0.45(100) + 0.40 x2 = 165

=> x2 = (165 - 45)/0.40 = 120 / 0.40 = 300

Therefore <x1,x2> = <100,300>

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.