Question

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.

Answer 1

the cost to produce x scooters is
C = 750 + 300x
Price of one scooter is
P = 900-x
profit = sales price of x scooters - cost
profit = x(900-x) - 750 - 300x
profit = 900x - x^2 - 750 - 300x
profit = -x^2 +600x -750
maximum profit is got by differentiating the above equation with respect to x and setting it to 0
d(profit) / dx = -2x +600
-2x+600 = 0
2x = 600
x = 300
so the company must produce 300 scooters to maximize profit.
the price would then be 900 - x = 900 - 300 = $600
the maximum profit is 300(900-300) - 750 - 300*300

Answer 2

= $89250