An automobile dealer can sell 12 cars per day at a price of $20,000. He estimates that for each $300 price reduction he can sell two more cars per day. If each car costs him $17,000, and fixed costs are $1000, what price should he charge to maximize his profit? How many cars will he sell at this price?
An automobile dealer can sell 12 cars per day at a price of $20,000. He estimates that for each $300 price reduction he can sell two more cars per day. If each car costs him $17,000, and fixed costs are $1000, what price should he charge to maximize his profit? How many cars will he sell at this price?
Intermediate Algebra
10th Edition
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter4: Rational Expressions
Section4.CM: Cumulative Review Problem Set
Problem 48CM
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An automobile dealer can sell 12 cars per day at a price of $20,000. He estimates that for each $300 price reduction he can sell two more cars per day. If each car costs him $17,000, and fixed costs are $1000, what price should he charge to maximize his profit? How many cars will he sell at this price?
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Now, we can find the revenue function by multiplying the price function by the quantity function and simplifying.
R(x) | = | p(x)q(x) |
|
||
= | (20,000 − 300x)(12 + 2x) |
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