# Modify the original Grand Prix example as follows. Increase the demands at the regions by 200 each,.

Modify the original Grand Prix example as follows. Increase

the demands at the regions by 200 each, so that total demand is well above

total plant capacity. This means that some demands cannot be supplied. Suppose

there is a unit penalty cost at each region for not supplying an automobile.

Let these unit penalty costs be $600, $750, $625, and $550 for the four

regions. Develop a model to minimize the sum of shipping costs and penalty

costs for unsatisfied demands. (Hint: This requires a trick. Introduce a fourth

plant with plenty of capacity, and set its unit shipping costs to the

»

Modify the original Grand Prix example as follows. Increase

the demands at the regions by 200 each, so that total demand is well above

total plant capacity. This means that some demands cannot be supplied. Suppose

there is a unit penalty cost at each region for not supplying an automobile.

Let these unit penalty costs be $600, $750, $625, and $550 for the four

regions. Develop a model to minimize the sum of shipping costs and penalty

costs for unsatisfied demands. (Hint: This requires a trick. Introduce a fourth

plant with plenty of capacity, and set its unit shipping costs to the regions

equal to the unit penalty costs. Then interpret an auto shipped from this

fictitious plant to a region as a unit of demand not satisfied.)

»