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
