During the war with Iraq in $1991,$ the Terraco Motor Company

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.$Formulate $($ONLY$)$ 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.$********$pay attention to capacity not equal to

demand$*********$DO NOT copy from other chegg answers I DO NOT

understand them$********$only formulate no

solving$*****$