Your company manufactures two models of speakers, the Ultra Mini and the Big Sta

Question

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 pi_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(p_1, p_2) = 100,000 - 600p_1 + p_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(p_1, p_2) = 150,000 + p_2 - 600p_2. Find the prices for the Ultra Mini and the Big Stack that will maximize your total revenue. (Round your answers to two decimal places.)

Explanation / Answer

q1(p1,p2)=100000-600p1+p2

100000=600p1-p2 ..... 1.

q2(p1,p2)=150000+p1-600p2

150000= - p1+600p2 ......2

eqn 2. multiply by 600

600*150000=-600p1+600*600p2

90000000=-600p1+360000p2 ......3.

eqn 1 + 3

90100000=359400p2

p2=90100000/359400

p2=250.70

put p2 in eq 1

150000= - p1+600*250.70

p1=420

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