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
–x^{2}. Therefore, the profit function is P(x) = R(x)-C(x)
= (600x –x^{2})-( 750 +100x) = -150+500x
–x^{2}.

Now, we know that P(x) will be maximum when dP/dx = 0 and
d^{2}P/dx^{2} is negative. Here, dP/dx = 500-2x = 0
when x = 250. Also, d^{2}P/dx^{2} =-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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