SOLUTION: Suppose that the total revenue (in dollars) from the sale of x headphones is given by R(x) = 46x and that the cost (in dollars) of manufacturing x headphones is given by C(x) = 100

Question 1172100: Suppose that the total revenue (in dollars) from the sale of x headphones is given by R(x) = 46x and that the cost (in dollars) of manufacturing x headphones is given by C(x) = 100 − 30x + 110x2.
How many headphones (below 500) were sold if the profit was $12,650
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
revenue function is r(x) = 46x
cost function is c(x) = 100 − 30x + 110x^2
profit function is p(x) = r(x) - c(x)
that makes profit function as shown on the next line.
p(x) = 46x - (100 - 30x + 110x^2)
simplify to get:
p(x) = 46x - 100 + 30x - 110x^2
combine like terms to get:
p(x) = -100 + 76x - 110x^2
arrange the expression on the right side of the equation in descending order of degree to get:
p(x) = -110x^2 + 76x - 100
the graph of the profit function looks like this.

as you can see, the maximum profit is -86.873 when x = .345
that's not even close to a profit of 12,650.
there must be something wrong with the equations.
please check again to see if there was an error in the presentation of this problem.
if not, then i believe there is no way that a profit of 12,650 could be attained with these equations the way they are.

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