Q 12.29. As a manufacturer, you have to decide how many regional distributors to sign up. Serving a dis- tributor costs more the farther away it is from the factory, and different distributors have different de- mand. By region, gross revenues and costs are (in millions of dollars) as follows:

There is no "time value of money" dimension in this problem.

1. Is it feasible to work out all possible combi- nations of distributors you can service? Is it sensible? 2. Which regions should you deliver to? 3. What is the total profit for serving them? 4. What is the marginal benefit and cost of serving the least profitable of your serviced distribu- tors? 5. What would be the marginal benefit and cost of serving one more distributor? 6. Now assume that to get into this business, you would also have to set up the factory. This would cost you a one-time up-front expense of $5 million. You can think of this as spreading the cost across distributors. How would this change your decision?

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Distributor A B C D E F G Gross Revenue $5 $4 $4 $3 $2 $7 $1 Cost $2 $2 $3 $4 $4 $5 $6