SOLUTION: Sharon's revenue "R" (in dollars) on the sale of "x" fruitcakes is determined by the formula R=50x-x^2. Her cost in "C" (dollars) for producing the x fruitcakes is given by the for

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Question 60986: Sharon's revenue "R" (in dollars) on the sale of "x" fruitcakes is determined by the formula R=50x-x^2. Her cost in "C" (dollars) for producing the x fruitcakes is given by the formula C=2x+40. For what values of x is Sharon's profit positive? (Profit=revenue-cost)
Answer by Nate(3500) (Show Source):
You can put this solution on YOUR website!
When your profit is zero, you receive as much money as you spent. So you want a profit greater than zero.
Profit > 0
Revenue - Cost > 0
50x - x^2 - 2x - 40 > 0
-x^2 + 48x - 40 > 0

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=2144 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 0.848326194419549, 47.1516738055805. Here's your graph: