AI Dale is planning his Christmas shopping for seven people. To quantify how much his various relatives would enjoy receiving items from a list of prospective gifts, AI has assigned appropriateness units (called "ohs") for each gift if given to each of the seven people. A rating of 5 ohs represents a gift that the recipient would really like. A rating of 4 ohs indicates the recipient would like it four-fifths as much; 3 ohs, three-fifths as much, and so forth. A zero rating indicates an inappropriate gift that cannot be given to that person. The objective is to select the most appropriate set of gifts for the seven people (that is, maximize total ohs) that can be obtained with the selected budget.
(a) How much will it cost to buy the seven gifts the people would like best, if there is ample money for Christmas shopping?
(b) If the Christmas shopping budget is set at $112, which gifts should be purchased, and what is their total appropriateness rating in ohs?
(c) If the Christmas shopping budget must be cut to $90, which gifts should be purchased, and what is their total appropriateness rating in ohs?