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
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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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