Please answer Exercises 1-4

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The Diet Problem The Galaxy Nutrition health-food mega-store chain provides free online nutritional ad- vice and support to its customers. As Web site technical consultant, you are plan- ning to construct an interactive Web page to assist customers in preparing a diet tailored to their nutritional and budgetary requirements. Ideally, the customer would select foods to consider and specify nutritional and/or budgetary constraints, and the tool should return the optimal diet meeting those requirements. You would also like the Web page to allow the customer to decide whether, for instance, to find the cheapest possible diet meeting the requirements, the diet with the lowest number of calories, or the diet with the least total carbohydrates. After doing a little research, you notice that the kind of problem you are trying is solve is quite well known and referred to as the diet problem, and that solving the diet problem is a famous example of linear programming. Indeed, there are already some online pages that solve versions of the problem that minimize total cost, so you have adequate information to assist you as you plan the page. You decide to start on a relatively small scale, starting with a program that uses a list of 10 foods, and minimizes either total caloric intake or total cost and satisfies a small list of requirements. Following is a small part of a table of nutritional infor mation from the demo at the NEOS Wiki (all the values shown are for a single serving) as well as approximate minimum daily requirements