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The revenue each season from tickets at the theme part is represented by t(x) = 5x. The cost to pay the employees each season is represented by r(x) = (1. 5)x. Examine the graph of the combined function for total profit and estimate the profit after four seasons.

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MrRoyal

The total profit after four seasons is 35.0

Function

The functions are given as:

  • Revenue function: [tex]t(x) = 5x[/tex].
  • Cost function: [tex]r(x) = 1.5x[/tex].

Profit function

The profit function p(x) is calculated using:

[tex]p(x) = t(x) -r(x)[/tex]

So, we have:

[tex]p(x) = 5x -1.5x[/tex]

Evaluate the differences

[tex]p(x) = 3.5x[/tex]

Total Profit

Evaluate the values of the function from x =1 to 4

  • [tex]p(1) = 3.5[/tex].
  • [tex]p(2) = 7.0[/tex].
  • [tex]p(3) = 10.5[/tex].
  • [tex]p(4) = 14.0[/tex]

So, the total profit is:

[tex]Total =p(1) + .....+p(4)[/tex]

This gives

[tex]Total =3.5 + 7.0 + 10.5 +14.0[/tex]

[tex]Total =35.0[/tex]

Hence, the total profit after four seasons is 35.0

Read more about profit, cost and revenue at:

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