Please read the question carefully before giving your answer. Only the techniques that you have learned in the course will be accepted! Q1. (25 pts) Cargoes from city i to city 6 are transported as follows: The cargo is sent first to either City 2 or City 3, then routed through either City 4 or City 5, and finally sent to City 6. The maximum number of cargoes that could be shipped from City i to j is shown below. For example; maximum of 500 cargoes can be sent from City 1 to City 2. The ultimate goal is to maximize the number of cargoes that is sent from City i to City 6 at any given time. 1-2 1-3 2-4 2-5 3-4 3-5 4-6 5-6 Cargo Capacity 500 400 300 250 200 150 400 350 a) Formulate an MCNFP for the above problem. (Give the mathematical model) Note: Formulate your model in an open form and while formulating it, give index (or indices), decision variable(s) and parameter(s), explicitly to receive credits. b) Determine whether the solution below is optimal or not. The numbers on arcs represent the amount of goods shipped through arc (1,3). Hint: The cost parameter (c_ij) for the arcs in this specific type of problem is equal to zero. 300 2. 4 500 400 100 1 6 250 200 350 150 3 5 750 Please read the question carefully before giving your answer. Only the techniques that you have learned in the course will be accepted! Q1. (25 pts) Cargoes from city i to city 6 are transported as follows: The cargo is sent first to either City 2 or City 3, then routed through either City 4 or City 5, and finally sent to City 6. The maximum number of cargoes that could be shipped from City i to j is shown below. For example; maximum of 500 cargoes can be sent from City 1 to City 2. The ultimate goal is to maximize the number of cargoes that is sent from City i to City 6 at any given time. 1-2 1-3 2-4 2-5 3-4 3-5 4-6 5-6 Cargo Capacity 500 400 300 250 200 150 400 350 a) Formulate an MCNFP for the above problem. (Give the mathematical model) Note: Formulate your model in an open form and while formulating it, give index (or indices), decision variable(s) and parameter(s), explicitly to receive credits. b) Determine whether the solution below is optimal or not. The numbers on arcs represent the amount of goods shipped through arc (1,3). Hint: The cost parameter (c_ij) for the arcs in this specific type of problem is equal to zero. 300 2. 4 500 400 100 1 6 250 200 350 150 3 5 750