For most products higher prices result in decreases demand whereas lower prices result in increased demand. Let d = annual demand for a product in units and p = price per unit.

Assume that a firm accepts the following price-demand relationship as being a realistic representation of the market:  

d=800-p   where p must be between $20 and $70

a. How many units can the firm sell at the $20 per unit price? At the $70 unit price?

b. What happens to annual units demanded for the product if the firm increases the per unit price from $26 to $27? From $42to $43? From $68 to $69? What is the suggest relationship between per unit price and annual demand for the product in units?

c. Show the mathematical model for the total revenue which is the annual demand multiplied by by the price per unit.

d. Based on other considerations the firms management will only consider price alternatives of $30, $40, and $50. Use your model from part b to determine the price alternative that will maximize the total revenue.

e. What are the expected annual demand and the total revenue according to your recommended price?