In preparing for a 7-day space shuttle mission
In preparing for a 7-day space shuttle mission, NASA must decide how many of each of six items should be loaded into the shuttle’s payload bay. The weight (in kilograms) and perceived benefit (where a larger benefit value indicates a more useful item) of each of the items are given below in Table 2. The shuttle can safely carry no more than 1200 kilograms of these items, given the various pieces of equipment and supplies that have already been loaded into the vehicle.In trying to decide what should be taken on the mission, NASA must ensure the following: (a) if any units of item type 1 are brought on board, then at least one unit of item type 5 must brought on board; (b) if any units of item type 2 are brought on board, then no units of item type 6 can be brought on board; (c) no more than four different types of items must be brought on board; and (d) units of item 3 or item 4 can be brought along but not both of these item types.Formulate and solve an appropriate decision model to help NASA decide how many units of each type of item to take on the mission in order to maximize the total benefit to be achieved. Present your solution in the report with an intuitive interpretation. (Hint: Items loaded cannot be real numbers.)Table 2 Data for Mission ItemsItem 1Item 2Item 3Item 4Item 5Item 6Benefit9.0113.5115.3217.1225.2319.82Weight304050607060
