Problem 2 - Network Model You've just started a job at a company that produces and distributes products around 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 Toledo, Cleveland, and Steubenville, OH. The distribution centers are located in Marion and Newark, OH. The retail locations are located in Columbus and Dayton, OH. A map of these nodes can be seen below: Toledo Bowling. Sandusky Green Findlay Lima Dayton Springfield Middletown Hamilton Cincinnati Mansfield. Marion Cuyahoga Falls OHIO Newark Cleveland Lancaster Warren. Youngstown. Akron Canton Steubenville Columbus Zanesville W VIRI costs associated with transporting a single unit of product between cities can be found in the table below: Destination Source Node 1 - Toledo Node 2 - Cleveland Node 3 - Steubenville Node 4 - Marion Node 5 - Newark Node 4 - Marion $119 $113 $120 Node 5 - Newark $103 $110 $107 Node 6 - Columbus $106 $78 Node 7 - Dayton $132 $91 Your boss tells you that the three factories (Toledo, Cleveland, Steubenville) each have different production capacities. They are 420, 470, and 455 units per week respectively. She also tells you that your retail stores have different levels of demand. Columbus has a demand of 710 units per week while Dayton has a demand of 620 units per week. Finally, each of the distribution centers can only handle 670 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