SOLUTION: Suppose that the equation p(x) = -2x^2 + 280x - 1000, where x represents the number of items sold, describes the profit function for a certain business. How many itmes should be so

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Suppose that the equation p(x) = -2x^2 + 280x - 1000, where x represents the number of items sold, describes the profit function for a certain business. How many itmes should be so      Log On


   

Question 57210: Suppose that the equation p(x) = -2x^2 + 280x - 1000, where x represents the number of items sold, describes the profit function for a certain business. How many itmes should be sold to maximize the profit?
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose that the equation p(x) = -2x^2 + 280x - 1000, where x represents the number of items sold, describes the profit function for a certain business. How many itmes should be sold to maximize the profit?
This is a parabolic function that opens down, its highest point is it's vertex. This parabolic function is in standard form: p%28x%29=ax%5E2%2Bbx%2Bc. To find the x value of the vertex, use the formula: x=-b%2F2a
In your case, a=-2, b=280, and c=1000
The number of items that should be sold to maximize the profit is:
x=-%28280%29%2F%282%28-2%29%29
x=-280%2F-4
highlight%28x=70%29
Happy Calculating!!!