What are the objective functions and variables for each option?

Case 3-1 Shipping Wood to Market Unit Investment for Ships ($1,000s) to Market Source 1 2 3 4 5 Alabama Atlantic is a lumber company that has three sources of wood and five markets to be supplied. The annual availability of wood at sources 1, 2, and 3 is 15, 20, and 15 million board feet, respectively. The amount that can be sold annually at mar- cets 1, 2, 3, 4, and 5 is 11, 12, 9, 10, and 8 million board feet, respectively. In the past, the company has shipped the wood by train. However, because shipping costs have been increasing, the alternative of using ships to make some of the deliveries is being nvestigated. This alternative would require the company to nvest in some ships. Except for these investment costs, the ship- ping costs in thousands of dollars per million board feet by rail and by water (when feasible) would be the following for each "oute. 275 293 WN - 303 318 283 238 270 275 250 268 285 265 240 Considering the expected useful life of the ships and the time value of money, the equivalent uniform annual cost of these investments is one-tenth the amount given in the table. The objec- tive is to determine the overall shipping plan that minimizes the total equivalent uniform annual cost (including shipping costs). Unit Cost by Rail ($1,000s) to Market Unit Cost by Ship ($1,000s) to Market Source 1 2 3 4 5 1 2 3 4 5 1 2 3 61 69 59 72 78 66 45 60 63 55 49 61 66 56 47 31 36 38 43 33 24 28 36 24 32 35 31 26 The capital investment in thousands of dollars) in ships 'equired for each million board feet to be transported annually by ship along each route is given next. You are the head of the management science team that has been assigned the task of determining this shipping plan for each of the three options listed next. Case 5-2 Capacity concerns Option 1: Continue shipping exclusively by rail. Option 2: Switch to shipping exclusively by water (except where only rail is feasible). Option 3: Ship by either rail or water, depending on which is less expensive for the particular route. Finally, consider the fact that these results are based on cur- rent shipping and investment costs, so that the decision on the option to adopt now should take into account management's projection of how these costs are likely to change in the future. For each option, describe a scenario of future cost changes that would justify adopting that option now. Present your results for each option. Compare