SOLUTION: Can someone help me out, please? Thank you! The owners of a parking garage have determined that their weekly revenue and cost in dollars are given by the following: R(x) =

Question 153209: Can someone help me out, please? Thank you!

The owners of a parking garage have determined that their weekly revenue and cost in dollars are given by the following:
R(x) = 56x - 2x^2
C(x) = 24x + 101
find the break even point.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Remember,

Profit = Revenue - Cost

which is symbolically:

Plug in and

Distribute the negative.

Combine like terms

Now the break even point occurs when you neither gain money nor lose money. In other words, break even point happens when the profit is zero. So this means that the break even point occurs when

Plug in

Notice we have a quadratic equation in the form of where , , and

Let's use the quadratic formula to solve for x

Start with the quadratic formula

Plug in , , and

Square to get .

Multiply to get

Subtract from to get

Multiply and to get .

Simplify the square root (note: If you need help with simplifying square roots, check out this solver)

or Break up the expression.

So the answers are or

which approximate to or

So the break even points occur when the price is either $4.33 or $11.67
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