Chapter 8.3, Problem 45E

Revenue Your company manufactures two models of speakers, the Ultra Mini and the Big Stack. Demand for each depends partly on the price of the other. If one is expensive, then more people will buy the other. If $p_{{}_1}$ is the price of the Ultra Mini and $p_{{}_2}$ is the price of the Big Stack, demand for the Ultra Mini is given by

$q_1\left(p_1,p_2\right)=100,000-100p_1+10p_2$, where $q_1$ represents the number of Ultra Minis that will be sold in a year. The demand for the Big Stack is given by

$q_2\left(p_1,p_2\right)=150,000+10p_1-100p_2$.

Find the prices for the Ultra Mini and the Big Stack that will maximize your total revenue.