l(q)= r(q)-c(q)= -0.0 1q^2+ 10q-(5q+200)

= -0.0 1Q^2 + 5Q - 200

To maximize profits, in addition to the book method, you can also find derivative method:

dL/dQ = -0.02Q + 5，

Let dL/dQ = 0 and get Q = 250.

d^2 l/dq^2 =-0.02 & lt； 0

Then Q = 250 is the only maximum point,

The maximum value l < max > =-0.01* 250 2+5 * 250-200 = 425.