Quadratic Polynomial Profit Problem

Question

For a certain company, the cost for producing x items is 55x+300 and the revenue for selling x items is 95x−0.5x^2.

 

The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit!

 

Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)

 

Part b: Find two values of x  that will create a profit of $300.

 

 

 

Part c: Is it possible for the company to make a profit of $15,000?

Answer 1

Part a: Profit P(x) = R(x) - C(x) = 95x - 0.5x² - 55x - 300 = 40x - 0.5x² - 300;

Part b: P(x) = 40x - 0.5x² - 300 = 300; x² - 80x + 1200 = 0; x = 20 or x = 60

Part c: P(x) = 40x - 0.5x² - 300 = 15000; x² - 80x + 30600 = 0; no real solution. So, profit can't be $15000