Chapter 12.6, Problem 23E

Modeling Exponential Demand As the new owner of a supermarket, you have inherited a large inventory of unsold imported Limburger cheese, and you would like to set the price so that your revenue from selling it is as large as possible. Previous sales figures of the cheese are shown in the following table:

$\text{Price per Pound,}p$	$3.00	$4.00	$5.00
$\text{Monthly Sales,}q\text{ (Pounds)}$	407	287	223

a. Use the sales figures for the prices $3 and $5 per pound to construct a demand function of the form $q=A{e}^{-bp}$, where A and b are constants you must determine. (Round A and b to two significant digits.)

b. Use your demand function to find the price elasticity of demand at each of the prices listed.

c. At what price should you sell the cheese to maximize monthly revenue?

d. If your total inventory of cheese amounts to only 200 pounds and it will spoil 1 month from now, how should you price it to receive the greatest revenue? Is this the same answer you got in part (c)? If not, give a brief explanation.