Small factory produces hand-crafted dolls; they observed that the demand function for the dolls can be approximated by q = 2000 – 40p.The fixed cost of operating the factory is $2500 per day.

Small factory produces hand-crafted dolls; they observed (based on historical data) that
the demand function for the dolls can be approximated by q = 2000 – 40p. The fixed cost of
operating the factory is $2500 per day. The variable cost of producing each doll during the day
shift (from 9am-5pm) is approximately $20. However, the variable cost of producing each doll
during the second shift (from 6pm – 2am) is $30. A maximum of 400 dolls can be produced in
each shift. (25 points)
(a) Write the function for the profit P(q).
(b) Sketch or plot a graph showing clearly the cost curve as well as the profit function.
(c) Find the quantity the factory should produce in order to maximize the profit.