Assume a firm has the following total cost function TC = 10Q2- 25Q + 150
(a) Specify the bounds of output and price for the function.
(b) Find the break-even points of output if the market price is $55.
(c) Find the profit maximizing level of output and show that it is the average of the two break-even points in part (b).
(d) Find the price and output when the total revenue line is tangent to the TC curve.
(e) Show that the market equilibrium price and the firm's output in the long run are the same as in part (d).