A company manufactures two products. For $1.00 worth of product A, the company spends $0.40 on materials, $0.20 on labor, and $0.10 on overhead. For $1.00 worth of product B, the company spends $0.50 on materials, $0.20 on labor, and $0.15 on overhead. Let
a = (0.40, 0.20, 0.10) b = (0.50, 0.20, 0.15)
Then a and b represent the "costs per dollar of income" for the two products. Suppose the company manufactures x dollars worth of product A and y dollars worth of product B and that its total costs for materials are $260, its total costs for labor are $120, and its total costs for overhead are $70.
Determine x and y, the dollars worth of each product produced.