Fitness Plus Fitness Plus is a full$-$service health and sports club in Greensboro, North Carolina. The club provides a range of facilities and services to support three primary activities; fitness, recreation and relaxation. In this case, Fitness Plus explores alternatives to expanding a new downtown facility. Fitness activities generally take place in four areas of the club, the aerobics room which can accommodate $35$ people per class; a room equipped with free weights; a workout room with $24$ pieces of Nautilus equipment; and large cardiovascular ; and a large cardiovascular workout room containing $29$ pieces of cardiovascular equipment. This equipment includes nine stairsteppers, six treadmills, six life$-$cycle bikes, three airdyne bikes, two cross$-$aerobics machines, two rowing machines, and one climber. Recreational facilities comprise eight racquetball courts, six tennis courts, and a large outdoor pool. Fitness Plus also sponsors softball, volleyball, and swim teams in city recreation leagues. Relaxation is accomplished through yoga classes held twice a week in the aerobics room, whirlpool tubs located in each locker room, and a trained massage therapist. Situated in a large suburban office park, Fitness Plus opened its doors in $1988.$ During the first two years, membership was small and use of the facilities was light. By $1992,$ membership had grown as Fitness began to play a large role in more and more people$$s lives. Along with this growth came increased use of club facilities. Records indicate that in $1992,$ an average of $15$ members per hour checked into the club during a typical day. Of course, the actual number of members per hour varied by both day and time. On some days during a slow period, only six to eight members would check in per hour. At a peak time, such as Mondays from $4$:$00$pm to $7$:$00$p$.$m$.,$ the number would be as high as $40$ per hour. The club was open from $6$:$30$am to $11$:$00$pm$.$ Monday through Thursday. On Friday and Saturday, the club closed at $8$:$00$pm$.,$ and on Sunday the hours were $12$:$00$ noon to $8$:$00$p$.$m$.$ As the popularity of health and fitness continued to grow, so did Fitness Plus. By May $1997,$ the average number of members arriving per hour during a typical day had increased to $25.$ The lowest period had a rate of $10$ members per hour; during peak periods $80$ members per hour checked in to use the facilities. This growth brought complaints from members about overcrowding and unavailability of equipment. Most of these complaints centered on the Nautilus, cardiovascular, and aerobics fitness areas. The owners began to wonder whether the club was indeed too small for its membership. Past research had indicated that individuals work out an average of $60$ minutes per visit. Data collected from member surveys showed the following facilities usage pattern: $30$ percent of the members do aerobics, $40$ percent use the cardiovascular equipment, $25$ percent use the Nautilus machines, $20$ percent use the free weights, $15$ percent use the racquetball courts, and $10$ percent use the tennis courts. The owners wondered whether they could use this information to estimate how well existing capacity was being utilized. If capacity levels were being stretched, now was the time to decide what to do$.$ It was already May, and any expansion of the existing facility world take at least four months. The owners knew that January was always a peak membership enrolment month and that any new capacity needed to be ready by then. However, other factors had to be considered. The area was growing both in terms of population and geographically. The downtown area had just received a major facelift, and many new offices and businesses were moving back to it$,$ causing a resurgence in activity. With this growth came increased competition. A new YMCA was offering a full range of services at a low cost. Two new health and fitness facilities had opened within the past year in locations $10$ to $15$ minutes from Fitness Plus. The first, called the Oasis, catered to the young adult crowd and restricted the access of children under $16$ years old. The other facility, Gold$$s Gym, provided excellent weight and cardiovascular training only. As the owners thought about the situation, they had many questions: Were the capacities of the existing facilities constrained, and if so$,$ where? If capacity expansion was necessary, should the existing facility be expanded? Because of the limited amount of land at the present site, expansion of some services might require reducing the capacity of others. Finally, owing to increased competition and growth downtown, was now the time open a facility to serve that market? A new facility would take six months to renovate, and the financial resources were not available to do both. $1.$ What method would you use to measure the capacity of Fitness Plus? Has Fitness Plus reached its capacity? $2.$ Which's capacity strategy would be appropriate for Fitness Plus? Justify your answer. $3.$ How would you link the capacity decisions being made by Fitness Plus to other types of operating decisions? The answer to question $1$ should include calculations, analysis of challenges and problems related to numbers, and opinion on the state of capacity $($no shortage vs$.$ timing problem vs$.$ quantity problem$).$Can you make a detailed calculation?