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For a certain company, the cost for producing x items is 50x + 300 and the revenue for selling x items is 90x - 0.5x^2.

The profit that the company makes is how much it takes in (revenue) minus how much it spend (cost). In economic models, one typically assumes that a company wants to maximize its profit or at least wants to make a profit:
Set up an expression for the profit from producing and selling x items
Find two values of x that will create a profit of $300

Respuesta :

Using the profit concept, we have that:

  • The expression is: P(x) = -0.5x² + 40x - 300.
  • A profit of $300 is found with x = 20 and x = 60.

What is the profit concept?

Profit is given by revenue subtracted by costs.

In this problem, we have that:

  • The revenue is: R(x) = 90x - 0.5x².
  • The costs are: C(x) = 50x + 300.

Hence the expression for the profit is given as follows:

P(x) = R(x) - C(x)

P(x) = 90x - 0.5x² - 50x - 300

P(x) = -0.5x² + 40x - 300.

A profit of $300 is found when P(x) = 300, hence:

300 = -0.5x² + 40x - 300

0.5x² - 40x + 600 = 0.

x² - 80x + 1200 = 0.

(x - 60)(x - 20) = 0.

Hence the values are:

  • x - 60 = 0 -> x = 60.
  • x - 20 = 0 -> x = 20.

More can be learned about the profit concept at https://brainly.com/question/4001746

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