The management at Easy loan 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 (Table 6.3) 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.

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Questions 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.

Table 6.3. Earls Court Gym: membership information Membership type Gym & Aerobics Full use of gym and all exercise classes, plus shower, sauna and changing facilities Gym only Unlimited use of gym and shower, sauna and changing facilities Period 12 months 9 months 6 months 5 months 4 months 3 months 2 months 1 month 3 weeks 2 weeks 1 week 1 day 12 months 9 months 6 months 5 months 4 months 3 months 2 months 1 month 3 weeks 2 weeks 1 week 1 day Earls Court Gym P.O.Box 755 254 Earls Court Road London SWS 9AD Tel: 020-7370 1402 Membership Rates Unrestricted access (ie. anytime during opening hours) New member Renewal 450 399 283 268 243 199 153 85 66 46 27 10 362 318 227 214 195 160 123 67 E53 38 21 3.50 (9 a.m. to 12 noon Mon. to Fri.) 5.00 (12 noon to 5 p.m. Mon. to Fri.) 7.50 (After 5 p.m. Mon. to Fri. and anytime Sat. and Sun.) 416 368 260 7 (Sat. & Sun.: 10) 335 294 211 Restricted access (i.e. Mon. to Fri. 9 a.m. to 5 p.m. & anytime at weekends) New member 292 261 182 172 158 129 99 54 44 30 20 232 210 145 139 127 103 81 44 35 24 16 Renewal 270 241 167 216 195 134