Silver scooter finds that it costs $300 to produce each scooter and the fixed costs are $750. the price is given by p=900-x, where p is the price in dollars at which exactly x scooters will be sold. find the quantity of scooters that the company should produce and the price it should charge to maximize profit. find the maximum profit.

Cost = 300 x + 750 , where x is the number of the scooters;
Price = 900 - x
Profit = x ( 900 - x ) - ( 300 x + 750 ) =
= 900 x - x² - 300 x - 750 = - x² + 600 x - 750
d (Profit) = - 2 x + 600
- 2 x + 600 = 0
x = 600 : 2
x = 300
The company must produce 300 scooters to maximize the profit.
The maximum profit is:
- 300² + 600 · 300 - 750 = $89,250