1. Consider the following information from a shipping network where there are two production plants and 4 outlets. The production, demand, capacity, and cost are shown below. Shipping Capacity and Demand Plant/production Outlet1 Outlet2 Outlet3 Outlet 4 Planti (400) 100 100 100 120 Plant2 (300) 50 200 100 200 Demand 100 200 150 250 Cost (in cents per item) Outlet 1 Plant 1 50 Plant 2 20 Outlet2 30 40 Outlet 3 20 40 Outlet 4 80 50 a. Formulate a minimum cost shipping schedule for this company. b. Use software to solve for the minimum cost and interpret the solution. State how many items will be shipped through each route. 2. Use the same information as in 1, but assume that you can ship to a central distribution center and then the distribution center can ship out to the outlets. The distribution center has a maximum capacity of 200 units than can be shipped. It costs 5 cents per item to ship from Plant 1 to the distribution center and 8 cents per item to ship from Plant 2 to the distribution center. The cost to ship from the distribution center to each outlet is given below: Outlet1 Outlet 2 Outlet 3 Outlet 4 DC 20 10 9 10 Add these additional constraints into your linear program from part 1 and find the new minimum cost shipping schedule. State the cost and interpret your solution