This is a Network flow problem, please solve a, b and c:

Stylen Company produces a popular custom accessory for smartphones, and now it must plan its production for the months of March and April. The accessories are produced at plants in Huntington and Bakersfield, and are shipped to distributors in New York City and Dallas. The plants in Huntington and Bakersfield have, respectively, the capacity to produce 3,000 and 4,000 units per month. For the month of March, the cost of shipping each unit is summarized in Table 2 . Table 2: Unit shipping cost (in \$) On April 1st, the shipping rates will each increase by $4.00 for products sent from Huntington, and decrease by $5.00 for products sent from Bakersfield. Each distributor has ordered 2,500 units of Stylen's products for the end of March, and 3,800 units for the end of April. Each distribution center can receive up to 1,000 extra units in addition to its demand in any month, but Stylen is contractually obligated to pay $3 per extra unit due to inventory costs. The company wants to develop a production and distribution plan for the months of March and April that would allow the company to meet the expected demand from each distributor at a minimum cost. (a) Draw a network flow model for this problem, including arc costs, lower/upper flow bounds, and excess flow. Hint 1: First draw a separate network flow model for each month. How are these two networks related? Using this relation, draw the arcs connecting the nodes of these two networks. As a final observation, remember to adjust the node names accordingly, i.e., each node must have a different name. Hint 2: You may find it easier to summarize the information (unit cost, lower bound and upper bound) for each arc in a table as opposed to writing it on your graph explicitly. (b) Write down the LP formulation corresponding to your graph. (Clearly define your decision variables, state your objective, and label your constraints.) (c) Implement your model in Excel. Report the optimal solution and value