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A break-even point is the intersection of the cost function and the revenue function, that is, where total cost equals revenue, and profit is zero. Mrs. Jones Cookies Store's cost and revenue, in dollars, for x number of cookies is given by C = .05x + 3000 and R = .80x. Find the number of cookies that must be sold to break even.

Respuesta :

Answer:

At break-even: [tex]x = 4000 \text{cookies}[/tex]

Step-by-step explanation:

given that:

[tex]C = 0.05x+3000[/tex]

[tex]R = 0.80x[/tex]

'x' is the number of cookies

the intersection of both of these lines is the break-even point.

hence,

C can be represented as:

[tex]y = 0.05x+3000\Rightarrow\,\text{A}[/tex]

and R can be represented as:

[tex]y = 0.80x\Rightarrow\,\text{B}[/tex]

now all we have to do is solve the equations simultaneously

substitute B into A

[tex]0.80x = 0.05x+3000[/tex]

[tex]0.80x = 0.05x+3000[/tex]

[tex]0.80x-0.05x =3000[/tex]

[tex]x = \dfrac{3000}{0.75} = 4000 \text{cookies}[/tex]

the number of cookies that must be sold to break-even is 4000