Question

silver scooter inc. finds that it costs$ 100 to produce each motorized scooter and that the fixed costs are $750. the price is given byp equals 600 minus x commap=600−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.

Answer 1

The variable cost of each motorized scooter produced by Silver scooter Inc. is $ 100. Also, the fixed costs are $ 750.

The selling price is given by p = 600−x , where x is the number of scooters sold. Then the cost function is C(x) = 750 +100x. Further, the revenue function is R(x) = px = (600-x)x = 600x –x². Therefore, the profit function is P(x) = R(x)-C(x) = (600x –x²)-( 750 +100x) = -150+500x –x².

Now, we know that P(x) will be maximum when dP/dx = 0 and d²P/dx² is negative. Here, dP/dx = 500-2x = 0 when x = 250. Also, d²P/dx² =-2 which is always negative regardless of the value of x. Hence, company should produce and sell 250 scooters ( at $ 600-250 = $ 350 each) to maximize profit. The maximum profit is -150+500*250 –(250)² = 125000-150-62500 = $ 62350.