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
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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.)

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