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An online retail company determined that their cost for each day, x, can be determined by the function c(x)=2x^2-20x+70 and their venue by the function R(x)=-x^2+5x+22. how many days willit take for the compant to earn profit?
i. 20
ii. 28
iii. 3
iv. 5

Answer :

Using the profit concept, it is found that the number of days that will take for the company to earn a profit is given by:

  • iii. 3

Profit:

  • Profit is given by revenue subtracted by costs.

In this problem:

  • The cost function is: [tex]c(x) = 2x^2 - 20x + 70[/tex].
  • The revenue function is: [tex]R(x) = -x^2 + 5x + 22[/tex].

Hence, the profit function is:

[tex]p(x) = R(x) - c(x)[/tex]

[tex]p(x) = -x^2 + 5x + 22 - (2x^2 - 20x + 70)[/tex]

[tex]p(x) = -3x^2 + 25x - 48[/tex]

Using a graphing calculator, it is found that the profit is positive after 3 days, hence, option iii is correct.

You can learn more about the profit concept at https://brainly.com/question/4001746

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