{c} Suppose now that at most 4WD cars may be shipped through Memphis and at most Elli!) cars may be shipped through Denver. 1. Write a constraint that would enforce this restriction. ii. 1Will the problem still be 31mm to have an integer solution {solving with LP]? [d] Suppose the company wanted to add a restriction that the number of cars shipped from Memphis to Atlanta plus the number of cars shipped from Denver to Los Angeles could be at most 3000. i. Write a constraint that would enforce this restriction. ii. 1Will the problem still be gimmibcd to have an integer solution {solving with LP]? 5. We focus now on a problem that can be solved using max flow. Suppose that you manage a job shop with l: identical machines, and have it jobs to process today. Each job i = 1,. . . ,1: requires p;- 2} 0 minutes of processing time on any machine, and has a processing window [unify] with s.- -i- p.- 3 iii. The job becomes available at time s.- and must be complete by its deadline d.-. A job can only be processed on one machine at a time, but it can be preempted; that is, its prooessing on one machine can be paused and later resumed on the same or another machine, as long as it finishes by its deadline. (a) Formulate a max flow model that determines if there exists a feasible processing sched ule. Present your network and state the condition to verify the existence of the feasible schedule. (Hint: Your network should have one node per job and nodes for interval of times. The number of machines may be included by using the capacities in the arcs.) {b} Consider k = 3 and use your formulation from {a} on the following example: I-III- Table 2 Example Use a solver to determine if there is a feasible schedule. Post an image of the output of the solver, and explicitly state if there is no feasible schedule (by listing the objec tive value] or give a feasible schedule [recovered from the solution of the max flow problem}. {c} 1What is the smallest amount of machines In that you need to get a feasible schedule? Justify your answer by providing a feasible solution for in and an explanation of why having only k" 1 machines does not lead to a feasible solution