# profit-maximizing price

Suppose a typical consumer's inverse demand function for bottled water at a resort area where one firm owns all the rights to a local spring is given by P = 15 - 3Q. The marginal cost for gathering and bottling the water is $3/gal. Find the optimal number of bottles to package together for sale and the profit-maximizing price to charge for the package. Find the solution and show it graphically.

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#### Solution Preview

The marginal revenue is MR = 15 - 6Q. To max its profit, the firm should produce at the level that MR = MC, i.e.,

15 - 6Q = 3

solve for Q = ...

#### Solution Summary

The expert identifies the profit-maximizing price. The inverse demand function is determined.

$2.19