Industria is having an event and needs to recruit student volunteers to help them sell beer. The volunteers can sign up to be either a Main bartender for any of the three 8 hour shifts or a Side bartender for one of the two 5 hour shifts. The main bartenders are paid 2 jetons per hour and the side bartenders 1 jeton per hour. Main bartenders can provide 50 beers per hour and side bartenders can provide 25 beers per hour. You can assume that the number of beer taps are not limiting the rate at which beer is served. Industria wants to keep the cost for the event as low as possible. The shift possibilities are given:

Main 1: 10h - 18h | Side 1: 14h - 19h

Main 2: 11h - 19h | Side 2: 15h - 20h

Main 3: 12h - 20h |

The following demand data is also available

10 h 5000 beers | 15 h 3000 beers

11 h 4000 beers | 16 h 4000 beers

12 h 3000 beers | 17 h 4500 beers

13 h 4000 beers | 18 h 3500 beers

14 h 2500 beers | 19 h 3000 beers

a) Formulate an LP in standard form to schedule the labour (6 pts) b) Two students have already said they want to work in the 12h - 20h shift, how would you adapt the LP? (1 pts) c) Panic! The supplier only delivered 100 beer taps. Industria wants as few people as possible to stand around without working, how would you adapt the problem to ensure as few people as possible are not working, while still meeting the beer demand? (3 pts) BONUS: Can you tell during which hours there will be more students than necessary?