Suppose that in tomato season there are three canneries under one management that ship cases of canned tomatoes to five warehouses. The number of cases processed at each cannery during the tomato season is known in advance as shown in the table below together with the cost to ship per case to each of the warehouses. Availability Shipping Cost ($/case) to of Warehouse Dump Canneries Cases a b c d e 1 50,000 0.9 2.0 1.8 1.7 2.5 1.0 2 75,000 0.6 1.6 1.4 1.8 2.5 1.0 3 25,000 2.7 1.8 1.5 1.0 0.9 1.0 The last column is the cost per case of dumping unshipped tomatoes. The seasonal demand, however, at each of the warehouses is uncertain. The probability distribution of demand is shown in the table below: Demand at Probability Warehouse .15 .55 .30 a 15,000 20,000 30,000 b 16,000 20,000 28,000 c 17,000 20,000 26,000 d 18,000 20,000 24,000 e 19,000 20,000 22,000 Cases left over at the end of the season cannot be stored until next year because the food in the cans will spoil. They must be shipped to the dump at a loss of $1 per case. Failure to supply all of the warehouses demands is penalized at $0.25 per case, the discounted estimated loss of all future sales. (Turning a customer away runs the risk that the customer will become the customer of another supplier.) What shipping schedule will optimize the sum of total shipping cost plus expected net revenues? Solve the problem in the following ways: (a) Formulate this as an equivalent deterministic linear program (EQ-LP). How many equations does this EQ-LP have? Solve this EQ-LP using any available software. (b) Solve EQ-LP using the method of Section 12.3. (c) Solve the problem using Benders Decomposition with crude Monte Carlo methods. (d) Solve the problem using Benders Decomposition with Monte Carlo methods using importance sampling.