A firm has the following total-cost and demand functions:
C=1/3Q³ - 7Q² + 111Q +50
Q= 100-P
a) Does the total-cost function satisfy the coefficient restrictions of (9.5 [a, c, d > 0 ; b<0 ; b²<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?