The cost, in dollars, for a company to produce x widgets is given by C ( x ) = 5250 + 7.00 x for x 0, and the price-demand function, in dollars per...

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

x ³ 0, and the price-demand function, in dollars per widget, is p(x) = 45 - 0.02x for 0 £ x £ 2250.

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.