The Green Grass Company manufactures and distributes a fertilizer product. The company sells its product to high-volume customers in various U.S. cities where it has manufacturing plants, but it can...

The Green Grass Company manufactures and distributes a fertilizer product. The company sells its product to high-volume customers in various U.S. cities where it has manufacturing plants, but it can decide to operate only some of these plants in any given month. The fixed monthly cost for operating any plant is $60,000, the plant capacity for any operating plant is 2500 pounds per month, and the production cost at any operating plant is $10.25 per pound. After the product is manufactured, it is shipped to customers at a rate of $0.02 per pound per mile. The cities and the distances between them are listed in Table 6.12. The customers submit order sizes and price bids to Green Grass, as listed in Table 6.13. For example, the customer in Boston requires an order of 1430 pounds this month and is willing to pay $75,740 for it. Green Grass can decide to fill this order or not. If not, we assume that the customer takes its business to another company. For the current month, Green Grass must decide which plants to operate and which customers to service from which operating plants to maximize its monthly profit.

Objective To develop a binary model to help Green Grass decide which manufacturing plants to operate and which customer orders to fill from which operating plants.