The deal your assistant signs calls for the sale of a minimum of 260 chairs and up to 410 chairs. The price will be $88 per chair if only 260 chairs are bought, but will be discounted by $0.2 per chair (on the entire order) for every chair ordered in addition to the minimum. Answer the questions below, rounding your answers to the nearest whole dollar.

Question

The deal your assistant signs calls for the sale of a minimum of 260 chairs and up to 410 chairs. The price will be $88 per chair if only 260 chairs are bought, but will be discounted by $0.2 per chair (on the entire order) for every chair ordered in addition to the minimum. Answer the questions below, rounding your answers to the nearest whole dollar.
a) What is the largest revenue you can make under this deal? 
revenue = $

b) What is the least revenue you can make under this deal? 
revenue = $

Steve · Answer

the domain is 260 <= x <= 410
the price per chair is 88.00 - 0.02(x-260)

revenue is price * quantity, so

R(x) = x(88.00-.02(x-260))
= 93.2x - .02x^2

For maximum revenue, just find the vertex of the parabola.

For minimum, figure the revenue at the two ends of the domain, and choose the least.