A canning company operates two canning plants, Plant A and Plant B. The growers that provide the fruits to this company are willing to supply fresh fruits in the following amounts:
• Supplier 1: 200 tons at $11/ton.
• Supplier 2: 310 tons at $10/ton.
• Supplier 3: 420 tons at $9/ton.
The Shipping costs in $ per ton are as follows:
From To Plant A Plant B
Supplier 1 3 3.5
Supplier 2 2 2.5
Supplier 3 6 4
The Plant capacities and labor costs are described in the following table:
Plant A Plant B
Capacity (tons) 450 560
Labor costs ($ per tons) 26 21
The canned fruits are sold at $50/ton to the distributors. The objective is to find the best mixture of the quantities supplied by the three growers to the two plants so that the company maximizes its profits. Formulate the problem as a linear program and explain it