Answer:
The factory should produce 166 pairs of high-grade shoes and 364 pairs of low-grade shoes for maximum profit
Step-by-step explanation:
The given parameters for the shoe production are;
The number of low grade shoes the factory produces ≥ 2 × The number of high-grade shoes produced by the factory
The maximum number of shoes the factory can produce = 500 pairs of shoes
The number of high-grade shoes the dealer calls for daily ≥ 100 pairs
The profit made per pair of high-grade shoed = Birr 2.00
The profit made per of low-grade shoes = Birr 1.00
Let 'H', represent the number of high grade shoes the factory produces and let 'L' represent he number of low-grade shoes the factory produces, we have;
L ≥ 2·H...(1)
L + H ≤ 500...(2)
H ≥ 100...(3)
Total profit, P = 2·H + L
From inequalities (1) and (2), we have;
3·H ≤ 500
H ≤ 500/3 ≈ 166
The maximum number of high-grade shoes that can be produced, H ≤ 166
Therefore, for maximum profit, the factory should produce the maximum number of high-grade shoe pairs, H = 166 pairs
The number of pairs of low grade shoes the factory should produce, L = 500 - 166 = 334 pairs
The maximum profit, P = 2 × 166 + 1 × 364 = 696
