If profit earned in the manufacture and sale of X units of a product is P dollars where:

P = 10X - 0.001X2

a) Sketch the profit function for appropriate values of X and P.

b) Find the maximum profit and the sales volume at which it occurs.

c) Find the sales volume or volumes which make profits equal to zero, (i.e. find the roots or the X-intercepts of the profit function).