5) A furniture business rents chairs for conferences. A conference can order fro

Question

5) A furniture business rents chairs for conferences. A conference can order from 300 to 500 chairs. The business charges a rental fee of $90 per chair per week. The business reduces the fee by $0.25 a a chair for every additional chair ordered above 300. This new rate is applied to all chairs in the order. Write an equation for the revenue function R(X); let x be the number of chairs ordered that are in excess of 300. Find the maximum revenue possible from one week's rental. How many chairs should be rented to produce the maximum revenue? Show all work and give an explanation for your answer.

Explanation / Answer

let the no. of chairs order be c

Revenue =

1. if c <= 300, revenue = 90c

2. if c >300, revenue = (90 - 0.25*(c-300)) * c = (90 - 0.25c +75) c = (165c - 0.25c2)

let's maximimze the f(c) = (165c - 0.25c2)

maximum value would occur at the point where first derivative is 0.

f'(c) = 165 - 0.50c = 0

c = 330

so maximum revenue would be at c = 330

which means x = 30

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