Problem \#2 (not from text) Consider a firm that, for simplicity, produces a single product. The firm has three plants (A,B and C), two warehouses ( Y and Z ) and four customers (1, 2, 3 and 4) geographically dispersed across the United States. As diagrammed in the figure below, the firm ships its product from a plant to a warehouse and then on to a customer In the above figure - The numbers to the left of each plant represent the plant's supply of the product. - The number to the right of each customer represent the customer's demand for the product. - The number written along an arrow drawn from a plant to a warehouse or from a warehouse to a customer is the corresponding unit shipping cost. For example, the shipping cost from plant C to warehouse Y is $25 per unit. The firm wants to distribute its product so it meets demand at the minimum cost. (a) Formulate an appropriate linear program. Parts (b)-(d) below are with respect to your answer in (a). Clearly specify the changes (i.e. if there is a change to a constraint - write the 'updated' constraint, if you add a new constraint - write it down as well, etc.) (b) How would you modify your LP from part (a) if the amount shipped between plant B and warehouse Y had to be at least 7 but at most 12 ? (c) How would you modify your LP from part (a) if the supply at plant C were increased to 20 , thereby creating excess supply? (d) How would you modify your LP from part (a) if the demand from customer 3 increased to 25 , thereby creating excess demand? (e) Optional for Extra Credit (up to 8pts: 2 pt for each part (a)-(d)). Use Excel solver to find the optimal shipping plan for each of the above scenarios (a)-(d). Remember to attach Excel files with your Submission in Blackboard