8) A firm faces a demand function = 720 8 (where =quantity demanded, and =price), and a total cost function = 25 + 15 + ² / 4 (where =output):

a) Manipulate the demand function to obtain an expression for in terms of . (2 marks)

b) Using the definition for total revenue, = , obtain an expression for in terms of only. (2 marks)

c) Obtain expressions for average revenue () and marginal revenue () in terms of . (3 marks)

d) Using the total cost () function you have been given, obtain an expression for average cost (), and marginal cost (). (4 marks)

e) Using the definition for profit, = , write down an expression for in terms of only. (2 marks)

f) Using optimisation, find the profit maximising level of output. (5 marks)

g) Show that this is a maximum point. (3 marks)

h) Using the expressions you have derived, calculate the level of output at which average cost () is minimized. (5 marks)