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 ...?

Question

Mathematics

Dahlia

2 March, 06:48

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 ...?

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Leo Patton · Answer 1

Cost = 300 x + 750, where x is the number of the scooters;

Price = 900 - x

Profit = x (900 - x) - (300 x + 750) =

= 900 x - x² - 300 x - 750 = - x² + 600 x - 750

d (Profit) = - 2 x + 600

- 2 x + 600 = 0

x = 600 : 2

x = 300

The company must produce 300 scooters to maximize the profit.

The maximum profit is:

- 300² + 600 · 300 - 750 = $89,250