A firm has the following total-cost and demand functions:

C=1/3Q^3 - 7Q^2 + 111Q +50

Q= 100-P

a) Does the total-cost function satisfy the coefficient restrictions of (9.5 [a, c, d > 0 ; b<0 ; b^2<3ac])

b) Write out the total-revenue function R in terms of Q

c) Formulate the total-profit function (pie) in terms of Q

d) Find the profit-maximizing level of output Q*

e) What is maximum profit?