The cost in dollars for a company to produce x widgets is gi

The cost, in dollars, for a company to produce x widgets is given by C(x) = 5250 + 7.00x for

In Quiz 2, problem #10, we saw that the profit function for this scenario is

              P(x) = - 0.02x² + 38.00x - 5250.

(a) The profit function is a quadratic function and so its graph is a parabola.

      Does the parabola open up or down? __________

(b) Find the vertex of the profit function P(x) using algebra. Show algebraic work.

Solution

a) We can decide whether parabola opens upward or downward with the a value in ax^2+bx+c.

if a> 0 => parabola opens upward and

if a< 0 => parabola opens downward

Now in P(x) = - 0.02x² + 38.00x - 5250      a= -0.02 < 0

Hence the parabola open down

b) P(x) = - 0.02x² + 38.00x - 5250

x- cordinate of vertex = -b/2a = - 38/-2*0.02 = 950

and y coordinate of vertex = -0.02(950)^2 +38*950 -5250 = 12800

Hence vertrx = (950, 12800)