Question

An automobile dealer can sell 12 cars per day at a price of $13,000. He estimates that for each $300 price reduction he can sell two more cars per day. If each car costs him $10,000, and fixed costs are $1000, what price should he charge to maximize his profit? [Hint: Let x = the number of $300 price reductions.]

Answer 1

Answer:

$ 1100

Step-by-step explanation:

Let p(x) be the price he charges for a car after x price reductions.

Since car costs him $10,000, and fixed costs are $1000

p(x) = 13000-10000-1000-300x = 2000 - 300x

Let  q(x) = 12 + 2x the quantity of cars sold after x price reductions.

and the profit he can make are given by:

Profit = R(x) = (12+2x)(13,000 - 10,000 - 1,000 - 300x) dollars.

As you can see, maximizing profit , we have to check where P'(x) = 0

And P''(x)<0.

So we get x = 3.

Replacing the value we get we get 2000 - 300 X 3 = 2000 - 900

                                                                  = $ 1100