13.the cost in dollars, for a company to produce x widgets is given by C(x)=5250=7.00x for x>=0, and the price demand function, in dollars per widget, is p(x)=45-0.02x for 0<=x<=2250.

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.

c) State the maximum profit and the number of widgets which yield that maximum profit:

The maximum profit is ______ when _______ widgets are produced and sold.

d) determine the price to change per widget in order to maximize profit.

e) Find and interpret the break-even points. (algebraic work)