Math Problem Statement

A company’s profit in dollars is given by the function P ( x )

5 x − 200 P(x)=5x−200, where x x represents the number of units sold. What is the company’s profit when they sell 50 units?

A) 250

B) 200

C) 150

D) 300

Solution

To calculate the company's profit when they sell 50 units, substitute x=50x = 50 into the profit function P(x)=5x200P(x) = 5x - 200:

P(x)=5x200P(x) = 5x - 200

Substitute x=50x = 50:

P(50)=5(50)200P(50) = 5(50) - 200

P(50)=250200P(50) = 250 - 200

P(50)=50P(50) = 50

Thus, the company’s profit is 50 dollars, which is not listed in the given options.

Could you confirm if the options provided are correct or clarify any additional information? If you'd like, I can help you re-check or adjust the options.


Would you like further details or have any questions? Here are 5 related questions:

  1. How is the slope 55 in the profit function significant?
  2. What happens to the profit when x<40x < 40?
  3. At how many units sold does the company break even?
  4. How would the profit function change if there was an additional fixed cost of $100\$100?
  5. What does a negative profit value imply in this context?

Tip: Always double-check provided options against calculated results to ensure accuracy!

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Profit Calculation

Formulas

P(x) = 5x - 200

Theorems

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Suitable Grade Level

Grades 7-9