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.

, 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.

(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 charge per widget in order to maximize profit.

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