Question

        A computer dealer can sell 12 personal computers per week at a price of $2000 each. He estimates that each $400 price decrease will result in three more sales per week. If the computers cost him $1200 each, what price should he charge to maximize his profit? How many will he sell at that price?

Answer 1

Let 'x' be the number of $400 decreases.

Then sold computers will be 12 + 3x, new price 1200 - 400x.

The equation profit earned by selling 12 + 3x computers at a price of 1200 - 400x is:

p = (12 + 3x)*(2000 - 400x) - (12 + 3x)*1200

p = -1200x^2 - 2400x + 9600

To find the max of the equation p = -1200x^2 - 2400x + 9600.

x max = -b/2a, where a = -1200, b = - 2400

x max = -(-2400)/(2*(-1200))

x max = 1

1200 - 400*1 = $800 per computer

12 + 3*1 = 15 computers

To maximize the profit he should charge $800 per computer. He will sell 15 computers at that price