You run a small furniture business. You sign a deal with a customer to deliver up to 700 chairs, the exact number to be determined by the customer later. The price will be $150 per chair up to 600 chairs, and above 600 the price will be reduced by $0.25 per chair (on the whole order) for every additional chair over 600 ordered. What is the largest revenue your company can make under this deal?

Question

I understand that the smallest revenue would be $0 since they could sell 0 chairs but I don't understand how to find the largest revenue.

I did R= (150-0.25x) (600+x)
so 90000-150x+150x-0.25x^2
so then 90000-0.25x^2 and you set that equal to 0... but then you just get 0 out of that? and that can't be the maximum revenue.

Answer 1

Your function is correct.
Maximum revenue is at x=0.
That means that an order for 600 chairs produces the maximum revenue.

This would not be the case if the discount were applied only to the excess chairs. Then the revenue would be

R(x) = 600*150 + x(150-.25x)
Then the maximum revenue would be at x=300. But the maximum order is 700 chairs, or x=100.

So, either way the problem seems flawed in its design.

Answer 2

Thank you so much for helping me!