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Your company manufactures two models of speakers, the Ultra Mini and the Big Stack. Demand for...

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 p1 is the price of the Ultra Mini, and p2 is the price of the Big Stack, demand for the Ultra Mini is given by

q1(p1, p2) = 100,000 − 500p1 + 10p2

where q1 represents the number of Ultra Minis that will be sold in a year. The demand for the Big Stack is given by

q2(p1, p2) = 150,000 + 10p1 − 500p2.

Find the prices for the Ultra Mini and the Big Stack that will maximize your total revenue. (Round your answers to two decimal places.)

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Answer #1

Q1 100,000 500p1 10p2 Or, P1 200-0.002Q10.02P2 TR1 P1Q1 200Q1- 0.00201+0.02p202 In order to maximize TR, set MR1 = 0 That is, 200-0.004010.02P2 (1) Similarly, MR2 300-0.004020.02P1-02) Equating (1) and (2), 200-0.00410.02P2 300-0.00420.02P1 Or, 0.02P2-0.00401-100 0.00402 0.02P1 Or, P2-0.2Q1 = 5000-0.2Q2 + P1 Or, 5P2-Q1 25000-Q2 + 5P1 Or, 5P2 -(100,000-500p1 10p2)-25000 (150,000 + 10pl- 500p2)+5P1 25000+500P1-5P25P1+500P2 25000 505P2 - 505P1 P2-P1-49.5 Thus, this condition can help solve the values of P1 and P2.

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