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 (quantity sold) for the Ultra Mini is given by q1 = 100,000 − 100p1 + 10p2 where q1 represents the number of Ultra Minis that will be sold in a year. The demand (quantity sold) for the Big Stack is given by q2 = 150,000 + 10p1 − 100p2. Find the prices for the Ultra Mini and the Big Stack that will maximize your total revenue. Remember that revenue for each item is price*quantity. (Round your answers to two decimal places.)

Principles of Accounting Volume 2
19th Edition
ISBN:9781947172609
Author:OpenStax
Publisher:OpenStax
Chapter3: Cost-volume-profit Analysis
Section: Chapter Questions
Problem 8EA: Marchete Company produces a single product. They have recently received the results of a market...
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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 (quantity sold) for the Ultra Mini is given by

q1 = 100,000 − 100p1 + 10p2

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

q2 = 150,000 + 10p1 − 100p2.

Find the prices for the Ultra Mini and the Big Stack that will maximize your total revenue. Remember that revenue for each item is price*quantity. (Round your answers to two decimal places.)

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