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A simple model of inventory management can be described as follows. Quantities of a certain part may be ordered to arrive at the beginning of cach month; there is a $12,000 fired cost per order, plus a holding cost of $50 for each part held in inventory cach month. The numbers of parts that are expected to be needed in production for the next 12 months are as follows: 4 50 5 180 1 60 2 120 3 100 6 250 7 160 8 70 9 40 10 100 11 110 12 60 If you order just 60 parts to arrive at the start of month 1, then you incur the $12,000 fixed cost, and you have to order again for the start of month 2. If you order three months' supply of parts to arrive at the start of month 2, then you incur the $12,000 fixed cost, plus a cost of 100 x $50 = $5,000 to keep 100 parts in inventory until month 3, plus a cost of 2 x 50 x $50 = $5,000 to keep 50 parts in inventory until month 4, for a total of $22,000; you don't need to order again until month 5. Your problem is to choose the sizes of the orders, so that the total order cost. plus holding cost is minimized. a: Describe how this type of inventory problem can be modelei as the problem of finding a shortest path in some particular network. Describe in words the nodes and arcs of the network, as well as the arc costs. b: Consider the inventory problem restricted to the first 6 months. Draw a pic- ture of the network for this particular case. c: Apply Dijkstra's method to solve the 6-month shortest-path problem. What is the minimum total fixed plus holding cost? To achieve this cost, in which periods must you order