The management at Easyloan Bank is interested in offering a corporate fitness programme for its employees. It has decided to offer a 50 per cent subsidy to all who participate. The gym has agreed to offer the bank a 20 per cent discount on all fees for its employees, provided that they all have the same terms of membership. The bank's management observe from the membership information that there are various membership options. From a survey of its employees it establishes that they would use the gym only. Of their visits, 75 per cent would be during weekdays and 25 per cent at weekends. Half their weekday visits would be before 12 noon and the other half would be after 5 p.m.
Question
1 Identify the feasible membership options and express these as cost functions for the bank.
2 Draw a graph showing the above options and explain how the bank's management should select the optimal one.