i = 1, ..., 30, j = 1, ..., 15, and t = 1, ..., 4

5. There are 30 Avengers working for Marvel film industry. Each of them might signed to 15 cuts in film, and they have 4 shifts. Assume that each Avengers is assigned to at most one plan in any given shift. We say that a plan is occupied if there is at least one Avenger. The decision variables of a mathematical programming model is: s1 Avenger i is assigned to film cut j during shiftt } Formulate on or more integer constraints that model the stated condition in each part below. Introduce, and clearly define, additional decision variables if necessary. (a) During each shift, there must be at least 3 Avengers on each film cut. Xije = { votherwise (b) On Plan B, Avengers 3, 6, and 9 cannot all work together on any shift C) The number of Avengers on film cut 5 must be the same for all shifts. (d) During shift 2, either film cut 7 and 8 are not taken yet, or a film cut 3 is taken