Consider the diet problem summarized in the following table. In this table, different food items available in a Mac Donalds restaurant are displayed in column A. Column B contains the selling prices of these food items (in dollars), and columns C,D,E and F contain their calories, protein contents (in grams), fat contents (in grams) and sodium contents (in milligrams), respectively. Columns G,H,I,J, K,L and M display various vitamin and mineral contents of the said food items (in % of Required Daily Allowances - RDA). Given that a "healthy" daily diet must contain, i) at least 55 grams of protein; ii) at most 3000 milligrams of sodium; iii) at least 100%RDA of vitamin A; iv) at least 100% RDA of vitamin C; v) at least 100% RDA of vitamin B1; vi) at least 100% RDA of vitamin B2; vii) at least 100% RDA of Niacin; viii) at least 100% RDA of Calcium; ix) at least 100% RDA of Iron; and that in such a healthy diet, x) no more than 30% of all calories should come from fat (1 gram of fat contains 9 calories); which food items (and how many) should be selected for daily consumption, in order to optimize various objectives, while satisfying the above constraints. * This problem is based on the article "Big Mac Attack Revisited", by E. Erkut, which appeared in OR/MS Today, pp. 50-52, June 1994. 1. (20 pts) Construct and solve L.P. models to minimize and maximize total daily cost. In the maximization case, comment on reasons of and ways to avoid unboundedness. Comment on the range defined by the minimum and maximum costs. 2. (10 pts) How valid is the continuity (of the decision variables) assumption. Comment on how violation of this assumption can be handled. 3. (20 pts) Comment on ways to divide a "minimal cost" diet into three courses (breakfast, lunch and dinner). Comment on how to generate "palatable and minimum cost" daily diets. Find the optimal solutions using Excel Solver. 4. (15 pts) Comment on how to achieve variety maximization (instead of cost minimization). Find the optimal solutions using Excel Solver. 5. (20 pts) Analysing the Excel Solver results, comment on including additional constraints to develop a "reasonable" diet, such as, - Either Egg McMuffin or Wheaties (for breakfast); - One order of French fries with each burger; - At least three drinks (milk or juice); - One milk with each Wheaties; - No more than two Wheaties; - In addition to any milk taken with Wheaties, at least two more drinks (milk or juice); - At least one salad; - No more packages of honey than the number of chicken. 6. (15 pts) Comment on trade-offs between different objectives such as cost minimization versus calorie minimization. Find the optimal solutions using Excel Solver