Question

# silver scooter inc. finds that it costs\$ 100 to produce each motorized scooter and that the...

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.

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.

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