I am required to submit the minimum number of people we need to recruit for our training centre. I heard Solver can help, but I am unable to figure out where to put the constraints and how to set them up since I never used Solver and the problem I have appears to be too complex and I hope solver can help. Hoping someone will help me. 
We have 7 locations with 3 classrooms at each location. We teach English, Math, Science, History, Economics. Classes run from 7 Am to 10 AM. 1030 AM to 130 PM. 2 PM to 5 PM. 530 PM to 830 PM. Each classroom can accommodate no more than 20 students although this is unimportant since I am trying to deduce the number of trainers I need. So technically all the three classrooms can be occupied at the same time which means I need 3 trainers for that time slot. And on any given day a trainer is required to take no less than 6 hours of classes and at most 9 hours of classes as you can see each class is 3 hours long. And trainers work 6 days a week. They dont work on Sunday.
English is the highest revenue subject for which we have may be 5-8 students in a class at most, again the number of students is not important but giving that info in case it is required.
Math is the lower revenue subject, for which we have the full strength of 20 students in the class.
History is the lowest revenue subject for which we have the full strength.
Science and economics are priced the same as History but not many students opt for it so there may be again only 3-5 students in the class.
Any class can be offered from Monday to Thursday or Friday and Saturday. So if you register for English from Monday to THursday, then your classes will be Monday, Tuesday, Wednesday and Thursday. If you register for English on Friday and Saturday, then your classes will be on Friday and Saturday only. So a trainer can teach from 7AM to 10 AM on all 6 days since students in M-THU class will be different from students in F-S class. That is true for all courses.
English trainers may also teach Math but not always. In Most cases they do, but if needed then we are ok with a trainer that teaches ONLY Math. If I am out of trainers that train students on both, then I will opt for recruiting trainers that teach only Math. History, Science and Economics are taught by the same person.
So we have three sets of trainers we are looking for. One that teaches English and Math. One that teaches Math only. One that teaches History/Science/Eco.
This is the problem.
I need to find the number of trainers we need if all the 3 classrooms are occupied at all the times. And we offer only one English class from M-THU, and one from F-S. We offer at least one or at most 3 Math Classes from M-T and at least one or at most 3 Math Classes from F-S . And we offer at least 1 or at most 2 History classes from M-THU and at least 1 or at most 2 History classes from F-S.
Am I asking for the moon? Or do I need Solver 2050?
Thanks so much for your kind help.
S
We have 7 locations with 3 classrooms at each location. We teach English, Math, Science, History, Economics. Classes run from 7 Am to 10 AM. 1030 AM to 130 PM. 2 PM to 5 PM. 530 PM to 830 PM. Each classroom can accommodate no more than 20 students although this is unimportant since I am trying to deduce the number of trainers I need. So technically all the three classrooms can be occupied at the same time which means I need 3 trainers for that time slot. And on any given day a trainer is required to take no less than 6 hours of classes and at most 9 hours of classes as you can see each class is 3 hours long. And trainers work 6 days a week. They dont work on Sunday.
English is the highest revenue subject for which we have may be 5-8 students in a class at most, again the number of students is not important but giving that info in case it is required.
Math is the lower revenue subject, for which we have the full strength of 20 students in the class.
History is the lowest revenue subject for which we have the full strength.
Science and economics are priced the same as History but not many students opt for it so there may be again only 3-5 students in the class.
Any class can be offered from Monday to Thursday or Friday and Saturday. So if you register for English from Monday to THursday, then your classes will be Monday, Tuesday, Wednesday and Thursday. If you register for English on Friday and Saturday, then your classes will be on Friday and Saturday only. So a trainer can teach from 7AM to 10 AM on all 6 days since students in M-THU class will be different from students in F-S class. That is true for all courses.
English trainers may also teach Math but not always. In Most cases they do, but if needed then we are ok with a trainer that teaches ONLY Math. If I am out of trainers that train students on both, then I will opt for recruiting trainers that teach only Math. History, Science and Economics are taught by the same person.
So we have three sets of trainers we are looking for. One that teaches English and Math. One that teaches Math only. One that teaches History/Science/Eco.
This is the problem.
I need to find the number of trainers we need if all the 3 classrooms are occupied at all the times. And we offer only one English class from M-THU, and one from F-S. We offer at least one or at most 3 Math Classes from M-T and at least one or at most 3 Math Classes from F-S . And we offer at least 1 or at most 2 History classes from M-THU and at least 1 or at most 2 History classes from F-S.
Am I asking for the moon? Or do I need Solver 2050?
Thanks so much for your kind help.
S
