(Solved): 1) A rock band is putting together a set list for their upcoming sig. They divide their songs into ...

1) A rock band is putting together a set list for their upcoming sig. They divide their songs into two categories: Bops and Ballads. Their repertoire includes 30 Bops and 20 Ballads. Bops last 3 minutes, while Ballads last 4 minutes. Their contract stipulates they must play between 2 and 3 hours (assume they play continuously from start to finish with no breaks). To keep the vibe right, they decide at least one third, but no more than half of the set list should be Ballads. The drummer notices each time they play a Bop, 10 people join the dance floor, and each time they play a Ballad, 5 people leave the dance floor (assume there are people on the dance floor to begin with). While still maintaining the aforementioned conditions, they decide to maximize the number of people on the dance floor. 1.a) Write out the objective function and constraints for this problem. 1.b) Sketch the feasible region and find the corner points. Evaluate the objective function at each of the corner points. 1.c) If the band maximizes dancers, and we assume people only join or leave the dance floor based on the band's songs, what is the net increase in dancers by the end of the gig? And how long does this gig last?