Calculus Question

Question

An office building owner agrees to buy a minimum of 270 chairs and up to 440 chairs from a supplier. The price will be $86 per chair if only 270 chairs are bought, but will be discounted by $0.25 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 the supplier can make under this deal? 

revenue = $

b) What is the least revenue the supplier can make under this deal? 

revenue = $

Answer 1

Let x: # of chairs ordered above 270. R(x): revenue (in $)

R(x) = (270 +x)·(86 - .25x) = -.25x² + 18.5x + 23,220 , 0 ≤ x ≤ 170

The revenue function is a concave down parabola with vertex/max at x = - b/2a = 37

Max revenue: R(37) = $23,562 (rounded to nearest dollar)

Since x = 170 is farther from the axis of symmetry than x = 0, the minimum revenue is at x = 170.

Min revenue: R(170) = $19,140