The XYZ Company has three plants producing child push chairs that are to be shipped to four distribution centers. Plants 1, 2, and 3 produce 13,15 , and 12 shipments per month, respectively. Each distribution center needs to receive 10 shipments per month. The distance from each plant to the respective distributing centers is given below: The freight cost for each shipment is $5 plus 50 cents per mile. How much should be shipped from each plant to each of the distribution centers to minimize the total shipping cost? a. Identify the objective function, decision variables and constrains for the problem of XYZ Company. b. Create the mathematical optimization models for the problem of XYZ Company. c. Obtain an initial solution using Northwest Corner and VAM. d. Obtain an optimal solution using Stepping Stone or Modified Distribution. e. Use optimization software to deciding how much should be shipped from each plant to each of the distribution centers to minimize the total shipping cost? f. Based on solutions at points c, d and e, please create the recommendations for Company XYZ