Solutions for problems whose numbers appear within a colored box can be found in the Student Solutions Files. Refer to this book's preface for purchase information.

Level A

In the original Grand Prix examp the total capacity of the three plants is $1550,$ well above the total customer demand. Would it help to have $100$ more units of capacity at plant $1?$ What is the most Grand Prix would be willing to pay for this extra capacity? Answer the same questions for plant $2$ and for plant $3.$ Explain why extra capacity can be valuable even though the company already has more total capacity than it requires.

The optimal solution to the original Grand Prix problem indicates that with a unit shipping cost of $$132,$ the route from plant $3$ to region $2$ is evidently too

expensive $-$ no autos are shipped along this route. Use SolverTable to see how much this unit shipping cost would have to be reduced before some autos would be shipped along this route.

Suppose in the original Grand Prix example that the routes from plant $2$ to region $1$ and from plant $3$ to region $3$ are not allowed. $($Perhaps there are no railroad lines for these routes.$)$ How would you modify the original model $($Figure $5\mathrm{.}3)$ to rule out these routes? How would you modify the alternative model $($Figure $5\mathrm{.}8)$ to do so$?$ Discuss the pros and cons of these two approaches.

In