Assume you are given a minimization linear program that has an optimal solution. The problem is then modified by changing an equality constraint in the problem to a less-than-or-equal-to constraint. Is it possible that the modified problem is infeasible? Answer yes or no and justify.

Suppose there are three types of consumers who attend concerts at your university’s performing arts center: students, staff, and faculty. each of these groups has a different willingness to pay for tickets; within each group, willingness to pay is identical. there is a fixed cost of $1,000 to put on a concert, but there are essentially no variable costs. for each concert: i. there are 140 students willing to pay $20. (ii) there are 200 staff members willing to pay $35. (iii) there are 100 faculty members willing to pay $50. a) if the performing arts center can charge only one price, what price should it charge? what are profits at this price? b) if the performing arts center can price discriminate and charge two prices, one for students and another for faculty/staff, what are its profits? c) if the performing arts center can perfectly price discriminate and charge students, staff, and faculty three separate prices, what are its profits?