Problem 3. (20%) Consider a transportation problem [ref. Lecture 2] specified by the following figure: Factory 1 Capacity. 20 Shop 1 Demand: 30 Factory 2 Capacity: 30 Shop 2 Demand: 40 Factory 3 Capacity: 40 Under the above configuration, we have the following requirements: . Factory 1, 2, 3 are producing a divisible product, and Shop 1, 2 are requesting the same product produced by the factories. The capacities and demands are specified as in the figure. . The cost of transporting I unit of product from factory i to shop j is as specified by the number next to the line connecting them, e.g., it costs $5 per unit to transport the product from factory 3 to shop 2. . The graph is not completely connected, e.g., Factory 3 cannot deliver to Shop 1 and Factory 1 cannot deliver to Shop 3. . It is possible to deliver product from a shop to a factory which will help alleviate the capacity limit on the factory. . The total transportation cost is calculated from the sum of absolute value of net amount of product delivered on all links, multiplied by the respective transportation cost per-unit. Homework 2 3 Answer the following question: (a) (10%) Formulate an optimization problem to minimize the total transportation cost while satisfying the demands raised by the shops and the capacities of the factories. In the optimization problem formulated, what are the decision variable(s)? what is the objective function? what is the constraint? (b) (10%) Reformulate the problem in part (a) as an LP in standard form