SOLUTION: The National Gizmo Corporation calculates that its profit, in thousands of dollars, on the sale of x thousand gismos is given by p(x)= -2x^2 + 52x + 30. How many gizmos must be sol

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: The National Gizmo Corporation calculates that its profit, in thousands of dollars, on the sale of x thousand gismos is given by p(x)= -2x^2 + 52x + 30. How many gizmos must be sol      Log On


   



Question 183984: The National Gizmo Corporation calculates that its profit, in thousands of dollars, on the sale of x thousand gismos is given by p(x)= -2x^2 + 52x + 30. How many gizmos must be sold in order to earn a maximum profit?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
p%28x%29=+-2x%5E2+%2B+52x+%2B+30
When he equation is of the form
y+=+ax%5E2+%2B+bx+%2B+c, the maximum occurs at
x+=+%28-b%29%2F%282a%29
b+=+52
a+=+-2
x+=+%28-b%29%2F%282a%29+=+%28-52%29%2F%282%2A%28-2%29%29
x+=+13
13 gizmos must be sold to maximize profit
I'll plot it
+graph%28+500%2C+500%2C+-6%2C+30%2C+-10%2C+400%2C+-2x%5E2+%2B+52x+%2B+30%29+