Phil\'s Tennis Emporium Club has six indoor tennis courts. Phil is perplexed abo
ID: 454722 • Letter: P
Question
Phil's Tennis Emporium Club has six indoor tennis courts. Phil is perplexed about how much time to set aside during the club's prime time hours this winter for each of the six revenue producing activities listed in the table below. Prime time is from 5:00 PM to 10 PM Sunday through Friday (i.e, each of the six courts is available for five hours per night, six nights per week). To satisfy club members, Phil has decided that at least one-half of the available prime time hours each week must be set aside for individual members play. A session for individual members takes up one hour of court time and produces $10 revenue as shown in the table below. Individual lessons by the head tennis pro, M. Hall, requires one hour and generates $30 revenue, while individual lessons by the assistant pro, D. Martin, requires one hour of court time and generates $25 revenue. M. Hall and D. Martin work together during each group sessions (i.e., both are present during an adult group lesson and both are present during a youth group lesson). Head pro M. Hall is only willing to work 30 hours per week, while assistant pro D. Martin is willing to work up to 60 hours per week. The demand dictates that no more than 20 individual lessons with the assistant pro should be scheduled during for the winter session. Phil believes that Youth Ciroup Lessons is an effective method to build membership in the club. Therefore Phil has decided to schedule at least two Youth group Lessons for every Adult Ciroup Lesson scheduled. Determine how many sessions of each of the six activities should be scheduled per week in order to maximize Phil's weekly revenue.Explanation / Answer
Legends
Assumptions, Workings and constraints
Answer 3a. Using above workings and optimizing revenue for club. This makes total weekly revenue of 2700.
Answer 3b. Question is not very clear. I'm assuming it meant revenue of head pro. More individual sessions (ILHP-1-30) are possible in only below scenarios
Answer 3c. If Head pro is willing to work 5 hours extra, then all this should be utilized for Individual Lession Head Pro (ILHP-1-30). But we have only 180 hours slot every week, so to maximize revenue, Individual Lession Assistant Pro (ILAP-1-25) should reduce by 1 (20 becomes 19 corrsponding to 1 hour) and League Play (LP-4-50) should also reduce by 1 (10 to 9 corresponding to 4 hours). League Play (LP-4-50) is reduced because revenue/hr is minimal among all except Individual Member Play (IMP-1-10) which cant be reduced below 50% of all the prime time slots.
This makes revenue earned by Individual Lession Head Pro (ILHP-1-30) for 11 sessions as 330, and overall revenue to be 2775, an increase of 75.
Answer 3d. Profit/hr for League Play (LP-4-50) is 50/4=12.5. This is minimum among all except Individual Member Play (IMP-1-10) and Group Lession Youth (GLY-2-40) which are 10/hr respectively. the next minimum is Group Lession Adult (GLA-2-75) at 18.75 (75/4). So the League Play revenue should be made atleast 76 to be more profitable making it 19/hr and better than (GLA-2-75)
Answer 3e. In the optimal revenue planning(3a), we are able to utilize only 44 hours (20 individual, 8 GLA and 16 GLY) of Assistant Pro, so this question and data won't change the maximum revenue which is pegged at 2700