The cost function to produce q electric cat brushes is given by C(q) = -10q + 250q.

The cost function to produce q electric cat brushes  is given by C(q) = -10q² + 250q. The demand equation is given by p = -q²- 3q + 299, where p is the price in dollars.

(a) Find and simplify the profit function.
(b) Find the number of brushes that will produce the maximum profit.
(c) Find the price that produces the maximum profit.
(d) Find the maximum profit.
(e) Find the point of diminishing returns for the profit function.