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An air-conditioning manufacturer produces room air conditioners at plants in Houston, Phoenix, and Memphis. These are sent to regional distributors in Dallas, Atlanta, and Denver. The shipping costs vary, and the company would like to find the least-cost way to meet the demands at each of the distribution centers while not exceeding the capacity at each plant. The table provides (1) the shipping costs from each plant to each destination, (2) the capacity at each plant, and (3) the demand at each destination. TO FROM 1. Dallas 2. Atlanta 3. Denver CAPACITY Houston $8 $12 $10 800 Phoenix $10 $14 $9 600 Memphis $11 $8 $12 300 DEMAND 600 400 200 Let H1, H2, H3, P1, P2, P3, M1, M2, and M3 represent the amounts shipped from Houston (H), Phoenix (P), and Memphis (M) to Dallas (1), Atlanta (2), and Denver (3) respectively. The associated linear program can be formulated as follows: Minimize cost = 8H1 + 12H2 + 10H3 + 10P1 + 14P2 + 9P3 + 11M1 + 8M2 + 12M3 Subject to: H 1 + P 1 + M 1 = 600 H 2 + P 2 + M 2 = 400 H 3 + P 3 + M 3 = 200 H 1 + H 2 + H 3 < 800 P 1 + P 2 + P 3 < 600 M1 + M 2 + M 3 < 300 All variables ≥ 0
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