1. The Scottish Claymore Company specializes in making replicas of the medieval Claymore sword for medieval battle reenactors. It has four production plants in Edinburgh, Glasgow, Dundee, and Inverness. The swords are all shipped to one of five distribution centers in London, New York, Boston, Paris, and Rome. The transportation costs (in dollars) between plants and distribution centers are as follows: London NY Boston Paris Rome Edinburgh 24.50 55.70 54.90 29.20 43.30 Glasgow 26.30 53.70 52.10 33.90 44.40 Dundee 27.50 55.10 60.60 32.40 46.20 Inverness 28.90 59.90 67.50 34.20 45.80 The maximum capacity of the Edinburgh plant is 1072; the capacity of the Glasgow plant is 959; the capacity of the Dundee plant is 920; and the capacity of the Inverness plant is 1250. The minimum required shipments to London, New York, Boston, Paris, and Rome are 785, 671, 752, 845, and 910, respectively. a. The company's objective is to minimize the cost of transporting its product from its plants to its distribution center while satisfying the above constraints. Write out the objective function and the constraints. b. Find the cost-minimizing solution using EXCEL's Solver. Hand in copies of the answer report and the sensitivity report. c. How do you interpret the shadow prices for the capacity constraints? Would it be profitable to add another unit of capacity to the Edinburgh plant if the cost of an additional unit of capacity is $3? Explain your answer with reference to the sensitivity report. d. Explain the value of Glasgow's shadow price with reference to the changing pattern of shipments if Glasgow had one more unit of capacity. e. Explain the value of Boston's shadow price with reference to the changing pattern of shipments if the minimum shipping requirement to Boston increased by one unit. f. By how much could the cost of shipping from Dundee to NY change by without changing your initial answer? Explain your answer with reference to the sensitivity report