Chapter 6.3, Problem 23E

In Exercises 15-22, assume that relative maximum and minimum values are absolute maximum and minimum values.

Two-variable revenue maximization. Rad Designs sells two kinds of sweatshirts that compete with one another. Their demand function are expressed by the following relationships:

$q_1=78-6p_1-3p_{2,}$

(1)

$q_2=66-3p_1-6p_{2,}$

(2)

Where $p_1$ and $p_2$ are the prices of the sweatshirts, in multiple of $10, and $q_1$ and $q_2$ are the quantities of the sweatshirts demanded, in hundreds of units.

a. Find a formula for the total-revenue function, R, in terms of the variables $p_1$ and $p_2$.

b. what prices $p_1$ and $p_2$ should be charged for each product in order to maximize total revenue?

c. How many units will be demanded?

d. What is the maximum total revenue?