Goodlife Gym in Mulgrave currently has 500 members but is planning on a membership drive to increase this number significantly using two strategies 1 and 2 and needs to determine the optimal membership level under each strategy.

Strategy 1 involves a partnership and paying Monash University pool facilities at Clayton $50 per gym member. Strategy 2 involves payment of a fixed fee of $100,000 per year for a massive advertising campaign.

The CEO has determined that the membership fee (price for gym membership) for the coming year will remain constant at $1,000 per member irrespective of the number of new members added and regardless of whether strategy 1 or 2 is adopted.

In the calculations for determining an optimal membership level, the CEO regards price as fixed; therefore, P = MR = $1,000. Before considering the effects of any agreement with Monash University, the CEO projects total cost function during the coming year to be as follows:

TC = $500,000 + $200Q + $0.2Q2

MC = TC/Q = $200 + $0.4Q

Where Q = number of gym members

a) Before considering the effects of the proposed agreement with Monash University under Strategy 1 or the marketing campaign under Strategy 2, calculate Goodlife's optimal membership and profit level. (3 Marks)

b) Calculate optimal (profit maximising) membership and profit levels under strategy 1. (3 Marks)

c) Calculate optimal (profit maximising) membership and profit levels under strategy 2. (3 Marks)

d) What should the CEO of Goodlife do to maximise profits? (1 Mark)