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Kimmie wants to earn money by baking and selling cookies. She works up a business plan and finds her cost and revenue functions whose graphs are shown above in green and red, respectively.

A). How many cookies must be produced and sold to break even?

B). What is the dollar amount coming in and going out if Kimmie just breaks even?

C).Use the formulas to write Kimmie's profit function, P(x), from producing and selling x cookies. (NOTE: Profit = Revenue - Cost)

D). How much profit will Kimmie earn if she produces and sells 520 cookies?

Kimmie wants to earn money by baking and selling cookies She works up a business plan and finds her cost and revenue functions whose graphs are shown above in g class=

Respuesta :

Using profit/cost/revenue concepts, it is found that:

  • a) 400 cookies must be produced and sold to break even.
  • b) The dollar amount coming in and going out is $400.
  • c) The profit function is [tex]P(x) = 2x - 800[/tex]
  • d) Kimmie will earn a profit of $240.

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  • The revenue function, that is, how much Kimmie earns selling x cookies, is given by: [tex]R(x) = 5x[/tex]
  • The cost function, that is, the cost of producing x cookies, is given by: [tex]C(x) = 800 + 3x[/tex]

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Question a:

The break even point is the value of x for which the revenue is the same as the cost, that is:

[tex]R(x) = C(x)[/tex]

Thus

[tex]5x = 800 + 3x[/tex]

[tex]2x = 800[/tex]

[tex]x = \frac{800}{2}[/tex]

[tex]x = 400[/tex]

400 cookies must be produced and sold to break even.

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Question b:

The dollar amount is [tex]R(400)[/tex].

[tex]R(400) = 5(400) = 200[/tex]

The dollar amount coming in and going out is $400.

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Question c:

Profit is revenue subtracted by cost, thus:

[tex]P(x) = R(x) - C(x)[/tex]

[tex]P(x) = 5x - (800 + 3x)[/tex]

[tex]P(x) = 5x - 800 - 3x[/tex]

[tex]P(x) = 2x - 800[/tex]

The profit function is [tex]P(x) = 2x - 800[/tex]

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Question d:

The profit earned is P(520), thus:

[tex]P(520) = 2(520) - 800 = 240[/tex]

Kimmie will earn a profit of $240.

A similar problem is given at https://brainly.com/question/24373628

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