SOLUTION: Please help. The demand for cabinets depends on the price per cabinet. A manufacturer determines that the number of cabinets he can sell is d= -3p^2 + 114p-240, where p is the pric

Algebra ->  Coordinate-system -> SOLUTION: Please help. The demand for cabinets depends on the price per cabinet. A manufacturer determines that the number of cabinets he can sell is d= -3p^2 + 114p-240, where p is the pric      Log On


   

Question 139750: Please help. The demand for cabinets depends on the price per cabinet. A manufacturer determines that the number of cabinets he can sell is d= -3p^2 + 114p-240, where p is the price per cabinet in dollars. At what price will the demand for cabinets be at a maximum?
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Your equation is in the form ax%5E2%2Bbx%2Bc with the value of a negative. This means you have a parabola that opens downward and that means that the vertex is the maximum point. The x-cordinate (actually the p-cordinate in this case) is the value of the independent variable that produces the maximum function value. So all you need to do to answer this question is find this value for the independent variable. This is easily calculated from the coefficients in the given equation. In general, the x-cordinate of the vertex is %28-b%29%2F2a. For your equation, a=-3 and b=114. Just substitute and do the arithmetic