Question

You run a small furniture business. You sign a deal with a customer to deliver up to 600 chairs, the exact number to be determined by the customer later. The price will be $130 per chair up to 500 chairs, and above 500, the price will be reduced by $0.25 per chair (on the whole order) for every additional chair over-ordered.

What is the largest revenue your company can make under this deal? What is the smallest revenue your company can make under this deal?

Answer 1

64,925‬

Minimum occurs at x = 0 when no chairs are sold. The price is $0.

Explanation:

solution

Let x be the number of chair greater than 500. Then price is

P = (130-0.25*x)(500 +x)

For critical point,

P'(x) = -0.5x + 15 = 0

From here, we get x = 30. Using second derivative test, P"(x) = -0.5 for all x so global maximum occurs as the function is concave downward. The price is

P(30) = (130 - 0.25*30)(500 + 30) = $64,925‬

Minimum occurs at x = 0 when no chairs are sold. The price is $0.