P(x) = - 0.015x² + 16.50x - 2137.50.

(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.