Super Sleep is a company making mattresses for king-size beds. Mattresses can be shipped directly from either of its plants to retail store customers, or they may be transshipped through the company's single warehouse. The table that follows shows the unit cost of shipping mattresses from the plants and the warehouse to Super Sleep's 2 customers. Shipping from either plant to the warehouse costs $15 per mattress. The table also shows the number of mattresses that can be produced at each plant over the next week and the number demanded by each customer. Plant 1 Plant 2 Warehouse Demand Shipping Costs Customer 1 Customer 2 30 23 14 700 25 45 11 160 Capacity 400 600 Super Sleep seeks a minimum total shipping cost way to supply its customers. Part a: Formulate a minimum cost flow model for this problem. Note: For this problem, you should provide a drawing of the minimum cost flow network. Explain in words what nodes and arcs represent, and label nodes and arcs with all relevant data. Problem 2: Suppose now that Super Sleep wishes to plan its shipping over a two-week time horizon. Customer demands remain 160 and 700 in the first week, but they are predicted to be 300 and 810 in the second. There is no initial inventory, but mattresses may be held in the warehouse for $10 per week. Due to size limitations, at most 120 mattresses can be held in the warehouse. All other parameters are the same in each week as those given in Problem 1. Complete part a (Hint: Let each node represent both a location and a time.)