A furniture business rents chairs for conferences. A contract is drawn to rent a

Question

A furniture business rents chairs for conferences. A contract is drawn to rent and deliver up to 400 chairs for a particular meeting. The exact number would be determined by the customer later. The price will be $90 per chair up to 300 chairs. If the order goes above 300 chairs, the price would be reduced by $0.25 per chair for every additional chair ordered above 300. This reduced price would be applied to the entire order. Determine the largest and smallest revenues this business can make under this contract.

Please show all work!!

Explanation / Answer

x = number of additional chairs

x <= 400-300 = 100

R(x) = (x+300)(90 - 0.25*x) = -1/4 x^2 + 25x + 27000

R'(x) = -x/2 + 25 = 0 -> x = 50 : maximum point

boundary points: x = 0 , x = 100

R(0) = 27000

R(50) = 350*(90 - 50/4) = 27125

R(100) = 27000

So

largest revenue = $27125

smallest revenue = $27000

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