# Calimex International is an agricultural company that has two primary regions for growing…

Calimex International is an agricultural company that has two primary regions for growing tomatoes, one in the Coachella Valley of California, the other in northern Mexico. During the peak season, tomatoes are picked daily and sent to one of three inspection stations in southern California. After the tomatoes have been inspected, they are transported to one of four packing houses.

Each day 4500 pounds of tomatoes are picked in California, and 4000 pounds are picked in Mexico. Each inspection station can process over 1 0 , 0 0 0 pounds per day. Since total daily supplies amount to only 8500 pounds, capacity at the inspection stations imposes no constraints on the shipments. That is, all tomatoes that arrive at any of the three inspection stations can be processed and sent on to the packaging plants. The packaging plants can handle 1500, 2500, 2000, and 2500 pounds per day, respectively.

The table for problem 3 gives the shipping cost per truck from each growing region to each inspection station and from each inspection station to each packaging plant; 500 pounds of tomatoes are shipped in each truck.

a. Find the shipping pattern that minimizes transportation costs from the growing area to the packaging plants.

b. Suppose a maximum of three trucks are available to travel each route. Which shipping pattern minimizes transportation costs from the growing areas to the packaging plants?

c. The situation modeled here consists of picking and loading tomatoes in the growing region, inspecting them at the inspection stations, and packing them at the packaging plants. Why might the assumption that the flow into the transshipment points (inspection stations) equals the flow out of the transshipment points be violated?

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