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.)