Problem 2 - Network Model You've just started a job a company that produces and distributes products around central Ohio. Your boss is struggling with the logistics of shipping your products in the most cost-effective way possible. She has tasked you with creating a network model in excel to help her out. Your logistics network consists of three factories, two distribution centers, and two retail stores. The factories are located in Lima, Mansfield, and Zanesville, OH. The distribution centers are located in Newark and Springfield, OH. The retail locations are located in Columbus and Dayton, OH. A map of these nodes can be seen below: 75 Ashland Delphos 30 Wooster Mansfield 30 Lima 1 Marion Mt Vernon 36 Sidney Coshock 3 Dublin Westerville Newark 03 Springfield 10 Zanesville Columbus 70 Grove City 1B Daxton Lancaster Beavercreek 05 35 Your boss tells you that all products MUST go through distribution centers before heading to retail stores. The costs associated with transporting a single unit of product between cities can be found in the table below: Destination Source Node 4 - Newark Node 6 - Columbus Node 7 - Dayton Node 1 - Lima $190 $83 Node 5 - Springfield $149 $68 Node 2 - Mansfield Node 3 - Zanesville $66 $124 Node 4 - Newark $96 $132 Node 5 - Springfield $75 $51 Your boss tells you that the three factories (Lima, Mansfield, and Zanesville) each have different production capacities. They are 400, 450, and 475 units per week respectively. She also tells you that your retail stores have different levels of demand. Columbus has a demand of 730 units per week while Dayton has a demand of 590 units per week. Finally, each of the distribution centers can only handle 700 units each week. Formulate a linear program and solve to find the ideal number of units that your company should strive to ship between locations each week, and the associated cost of it. Round all answers to two decimal places. You'll notice that the sheet for this problem is blank. We are expecting you to be able to create a linear program from scratch, with proper formatting that you have learned so far in this class. We will expect decision variables to follow the correct naming convention. For example: the decision variable that represents shipping a unit from node 1, to node 2 would be written as: X12