SOLUTION: Jesse Manufacturing estimates that its profit P in hundreds of dollars is P=-2x^2+20x-2 where x is the number of units produced in thousands. How many units must be produced to obt

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Jesse Manufacturing estimates that its profit P in hundreds of dollars is P=-2x^2+20x-2 where x is the number of units produced in thousands. How many units must be produced to obt      Log On


   

Question 277941: Jesse Manufacturing estimates that its profit P in hundreds of dollars is P=-2x^2+20x-2 where x is the number of units produced in thousands. How many units must be produced to obtain maximum profit?
a.500 units
b.5000 units
c.50 units
d.5 units
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
The graph of P=-2x%5E2%2B20x-2 is a parabola (because of the x squared) which opens downward (because of the minus in front of the x squared). It looks like this:
graph%28300%2C+300%2C+-5%2C+50%2C+-5%2C+50%2C+-2x%5E2%2B20x-2%29
The maximum of P will be at the vertex of the parabola. So we want to find the x coordinate of the vertex.

For a parabola in the form y+=+ax%5E2+%2B+bx+%2B+c, the x coordinate of the vertex is (-b)/2a. Since your b is 20 and your a is -2, the x coordinate of the vertex will be:
%28-%2820%29%29%2F2%28-2%29+=+%28-20%29%2F%28-4%29+=+5

So the answer is (d) 5 units.