Question 1167949
not sure if this is right, but this is what i get.


R = x * p


p = 118 - .045x


p in both equation equals the price per unit.


if you replace p in the first equation with its equivalent value of 118 - .045x, then you get:


R = x * (118 - .045x)


simplify to get:


R = 118 * x - .045 * x^2


if you replace R with y, the equation becomes y = 118 * x - .045 * x^2


y represents the revenue, just like R represented the revenue.


this allows the equation to be graphed more easily, since a lot of graphing software assumes the vertical axis is the y-axis and the horizontal axis is the x-axis.


if we reorder the terms in descending order of degree and switch sides, the equation remains the same, but is shown as:


-.045 * x^2 + 118 * x = y


if we want the revenue to be equal to 9200, we set y equal to 9200 and we get:


-.045 * x^2 + 118 * x = 9200


if we want to solve this quadratic equation, we subtract 9200 from both sides to get:


-.045 * x^2 + 118 * x - 9200 = 0


when we solve this quadratic equation, we get:


x = 80.43328924441 or x = 2541.7889329778


those values of x make the equation true.


if we add 9200 to both sides of the equation, the equation is still true.


we get:


-.045 * x^2 + 118 * x = 9200


what all this is saying is that when x = 80.43328924441 or x = 2541.7889329778, y = 9200, which is saying that the revenue is equal to 9200.


we have values of x, but we don't have values of p.


we know that x * p = revenue, so we solve for p by dividing 9200 by x.


we get:


9200 / 80.43328924441 = 114.38050198


9200 / 2541.7889329778 = 3.61949802


i didn't round because, if you wanted to check if the arithmetic is correct, you would have to use the unrounded numbers or you would come up with some small discrepancies.


i will round now, since i showed you what the unrounded numbers are.


the number of units probably should be rounded to the nearest unit.


the money probably should be rounded to the nearest penny.


after doing that, you get:


if you produce about 80 units, the price per unit should be about 114.38.


if you produce about 2542 units, the price per unit should be about 3.62 


both the demand equation and the revenue equation are satisfied when x = 80.43328924441 or x = 2541.7889329778


demand equation is p = 118 - .045 * x
when x = 80.43328924441, p = 114.38050198
when x = 2541.78893298, p = 3.61949802


revenue equation is r = x * p
when r = 9200, the equation becomes 9200 = x * p
when x = 80.43328924441, p = 114.38050198
when x = 2541.78893298, p = 3.61949802


both the demand equation and the revenue equation are satisfied with those number.


that's the best i can do.
i think it's right, but i always allow for the possibility that i could be wrong.


good luck with it.


hopefully this helps.