A firm faces a demand function q = 720 8p (where q=quantity demanded, and

p=price), and a total cost function TC = 25 + 15q +q²/4 (where q=output):

a) Manipulate the demand function to obtain an expression for p in terms of q.

b) Using the definition for total revenue, TR= pq, obtain an expression for TR in

terms of q only.

c) Obtain expressions for average revenue (AR) and marginal revenue (MR) in terms of q.

d) Using the total cost (TC) function you have been given, obtain an expression for average cost (AC), and marginal cost (MC).

e) Using the definition for profit, (pi) = TR TC, write down an expression for (pi) in terms of q only.

f) Using optimisation, find the profit maximising level of output.

g) Show that this is a maximum point.

h) Using the expressions you have derived, calculate the level of output at which

average cost (AC) is minimized.