SOLUTION: Ricky's Rockers, makes and sells wooden rockers. The daily revenue from the sale of those rockers is given by the function, R(x)=x^2-18x. Ricky Ray has determined that the daily co

Question 326602: Ricky's Rockers, makes and sells wooden rockers. The daily revenue from the sale of those rockers is given by the function, R(x)=x^2-18x. Ricky Ray has determined that the daily cost of producing his rockers is described by the function, C(x)=81+6x. How many rockers much Ricky's Rockers make and sell daily to break-even?
I have no clue where to even begin. Thank you so much for your help.
Answer by jessica43(140) (Show Source): You can put this solution on YOUR website!
In order for Ricky's Rockers to break-even (have positive revenue), the revenue must be greater than the costs. So you need to set up an inequality that has the revenue equation greater than the cost equation:
x^2 - 18x > 81 + 6x
Now, you need to solve for x. First let's combine all like terms:
x^2 - 18x > 81 + 6x
x^2 > 81 + 24x
x^2 - 24x - 81 > 0
Now we can try to factor this trinomial. Factoring a trinomial is the opposite of the FOIL method. The factors will have this form:
(x A)(x B)
where A and B will be the factors of the third term (-81). The factors of 81 are: 1, 3, 9, 27 and 81. We know that one of these factors must be negative because 81 is negative, so the possibilities of A and B are: -1&81, -3&27, -9&9, 1&-81, or 3&-27.
Now, we need to see what combination, when added, will equal -24 (since the second term is -24x).
The only possibility is 3 and -27.
So your answer is:
(x+3)(x-27) > 0
We know that for this equation to equal zero, x can equal -3 or 27. But for this equation to be greater than 0, x > 27 is the only solution.
This means that if Ricky's Rockers sells 27 rockers, they will make exactly $0. For them to break-even, they must sell greater than 27 rockers.
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