The Terraco Motor Company has produced a lightweight, all$-$terrain vehicle code$-$named $"$J$99$

Terra" for the military. The company is now planning to sell the Terra to the public. It has five

plants that manufacture the vehicle and four regional distribution centers. The company is unsure

of public demand for the Terra, so it is considering reducing its fixed operating costs by closing

one or more plants, even though it would incur an increase in transportation costs. The relevant

costs for the problem are provided in the following table. The transportation costs are per thousand

vehicles shipped; for example, the cost of shipping $1,000$ vehicles from plant $1$ to warehouse $C$

is $$32,000.$

GER PROGRAMMING

Formulate and solve an integer programming model for this problem to assist the company

in determining which plants should remain open and which should be closed and the number of

vehicles that should be shipped from each plant to each warehouse to minimize total cost.