Q1.1 (20 pts) - Creating a mathematical model The EG Manufacturing has three factories (Purple. Blue, and Orange) and three stores (Alpha. Beta, and Gamma). The following table shows the shipping costs between each factory and store, the factory manufacturing capabilities, and the store capacities. Management would like to keep the stores filled to capacity in order to generate demand. Table 1: Parameters Required for the Problem From To Alpha Beta Gamma Production Capacity Purple $6 $5 $3 Blue $10 $11 $14 5000 12000 Orange Demand $8 $18 7000 According to the given information answer the following a) (3p) Draw the network diagram of the given problem. b) (10p) Write a closed form mathematical model of the problem by defining following steps. i) (2p) Define decision variable(s) of the model. ii) (2p) Define sets and parameters of the model. iii) (2p) Write objective function of the model. iv) (4p) Write the constraint(s) of the model. a) Linear programming model b) Non-linear programming model 6000 8000 10000 c) Heuristic model d) Stochastic model c) (3p) Select the type of the mathematical model? What is the reason behind this selection? Explain with a few sentences. questions.

Q1.1 (20 pts) - Creating a mathematical model The EG Mannfacturing has three factories (Purple, Blue, and Orange) and three stores (Alpha. Beta, and Gamma). The following table shown the shipping costs between each factory and store. the factory mannfacturing capabilities, and the store capacities. Management wonld like to leep the stores filled to capacity in order to generate demand, Aecording to the given information amswer the followidg questions. a) (3p) Draw the network diagram of the given problem. b) (10p) Write a closed form mathematical model of the problem by defining following steps. i) (2p) Define decision varizble(s) of the model. ii) (2p) Define sets and parameters of the model. iii) (2p) Write objective function of the model. iv) (4p) Write the constraint (s) of the model. c) (3p) Select the type of the mathematical model? What is the renson behind this selection? Explain with a few sentences. a) Linear programming model b) Non-linear programming model c) Heuristic model d) Stochastic model