Silver Scooter inc finds that it costs 200 to produce each m

Silver Scooter inc. finds that it costs $200 to produce each motorized scooter and that the fixed costs are $1, 500. The price is given by = - 500 - 2x, 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. How many scooters should the company produce to max-we profit?

Solution

Given

$300 a scooter
$1500 fixed cost
p = 700 - 2x
p is price
x number of scooters sold

The profit is revenue - production cost

Pr = px - (200x + 1500)
= x(500 - 2x) - (200x + 1500)
= -2x^2 + 300x - 1500

Taking the derivative

Pr\' = -4x + 300

Setting it to zero

-4x + 300 = 0
x = 75

The quantity of scooters should be 75

The price should be

p = 500 - 2*75
= $350

The maximum profit will be

Pr = -2(75)^2 + 300(75) - 1500
=$9750