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Texts: An automobile dealer can sell 12 cars per day at a price of $14,000. He estimates that for each $300 price reduction he can sell two more cars per day. If each car costs him $11,000, and fixed costs are $1,000, what price should he charge to maximize his profit? How many cars will he sell at this price? Step 1: We need to find the number of cars at which the dealer will maximize his profit. To maximize the profit, we need to find the profit function. From the text, the profit function is given by P(x) = R(x) - C(x), where R(x) is the revenue, C(x) is the cost function, and x is the number of $300 price reductions. To find the revenue function, we multiply the quantity of cars sold by the price at which each is sold. First, we find the price function. Each car will sell for $14,000 minus x reductions of $300 each. Thus, the price function is p(x) = 14000 - 300x. The quantity that the dealer can sell is 12 plus 2 for each price reduction. Thus, the quantity sold is q(x) = 12 + 2x.

Name: texts an automobile dealer can sell 12 cars per day at a price of 14000 he estimates that for each 300 price reduction he can sell two more cars per day if each car costs him 11000 and fixed 29918
Uploaded: 2022-07-21T15:07:07-08:00
Duration: 5 min 46 s
Channel: Vishal Parmar
Description: texts an automobile dealer can sell 12 cars per day at a price of 14000 he estimates that for each 300 price reduction he can sell two more cars per day if each car costs him 11000 and fixed 29918

          Texts: An automobile dealer can sell 12 cars per day at a price of $14,000. He estimates that for each $300 price reduction he can sell two more cars per day. If each car costs him $11,000, and fixed costs are $1,000, what price should he charge to maximize his profit? How many cars will he sell at this price?

Step 1: We need to find the number of cars at which the dealer will maximize his profit. To maximize the profit, we need to find the profit function. From the text, the profit function is given by P(x) = R(x) - C(x), where R(x) is the revenue, C(x) is the cost function, and x is the number of $300 price reductions. To find the revenue function, we multiply the quantity of cars sold by the price at which each is sold. First, we find the price function. Each car will sell for $14,000 minus x reductions of $300 each. Thus, the price function is p(x) = 14000 - 300x. The quantity that the dealer can sell is 12 plus 2 for each price reduction. Thus, the quantity sold is q(x) = 12 + 2x.

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