Big Mac Questions 1-5 please.

SPRING 2020 IE 405 Project Descriptions The objective of this assignment is to start using a commercial code to solve an optimization problem and to be able to interpret the results provided by the solver. You should treat each question independently and solve using LINDO. And for those questions I ask you to comment, the solution output of LINDO is not sufficient, you have to interpret the results. Consider the diet problem summarized in the following table. In this table, different food items available in a McDonald's restaurant are displayed in column A. Column B contains the selling of these food items (in dollars), column C contain their calories (in cal), and columns D, E and F contain their 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). 2 26 121 Food Items Hamburger McLean Big Mac Small FF Chicken Honey Chef Salad Garden Salad Egg McMutin Wheaties Yogurt Milk Orange Grapefr. Apple . Helle882 6 BCDEFGHIJKLM Price Calorie Prot. Fat Sod.A C B1 B2 Nia. Calc Iron cal. 8. 3. mg. RDA 0.59 265 129 490442010201015 1.79 320 22 10 67010 1.65 S001 89061 0.68 2201 11001 1.56 2701 201 15 58001 45 01 0 0 2.69 170 171 400 1.96 50 1.36 28018 7101 1.09 9021 22020 0.63 10341 8021 0.3611092 130107 0.88 80101 01 01 1201 101 0.68 8000010042 0.68 90001 50 22 of 7 COLLE wola Care Me! 701 9 10 22908-98cool 12 13 14 15 Given that a "healthy" daily diet must contain, 1. at least 55 grams of protein; 2. at most 3000 milligrams of sodium; 3. at least 100% RDA of vitamin A; 4. at least 100% RDA of vitamin C; 5. at least 100% RDA of vitamin B1; 6. at least 100% RDA of vitamin B2; 7. at least 100% RDA of Niacin; 8. at least 100% RDA of Calcium; 9. at least 100% RDA of Iron; 10. no more than 30% of all calories should come from fat (1 g. of fat contains 9 cal. calories). Which food items and how many) should be selected for daily consumption, in order to optimize various objectives stated below, 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. SPRING 2020 IE 405 Big Mac Questions: 1. 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. 2. How valid is the continuity assumption in this real-life problem (according to continuity assumption, the decision variables can take non-integer values)? Comment on how the violation of this assumption can be handled. 3. Comment on ways to divide a "minimal cost" diet into three courses (breakfast, lunch and dinner) to generate "palatable and minimum cost" daily diets: come up with at least 5 constraints to generate palatable diets, e.g., Egg McMuffin or Wheaties can only be caten during breakfast, one order of French fries for each hamburger for lunch, no fries are caten during dinner. Hint: Decompose each singular variable xi, corresponding an individual food item i, into three variables (xil, xi2, xi3) corresponding to consumption levels at breakfast, noon and dinner, respectively. 4. Comment on how to deal with multiple objectives at the same time. Suppose that you want to minimize calorie intake and cost simultaneously. 5. (Bonus Question) Comment on how to achieve variety maximization instead of cost minimization). In order to model this scenario, you have to use integer variables. SPRING 2020 IE 405 Project Descriptions The objective of this assignment is to start using a commercial code to solve an optimization problem and to be able to interpret the results provided by the solver. You should treat each question independently and solve using LINDO. And for those questions I ask you to comment, the solution output of LINDO is not sufficient, you have to interpret the results. Consider the diet problem summarized in the following table. In this table, different food items available in a McDonald's restaurant are displayed in column A. Column B contains the selling of these food items (in dollars), column C contain their calories (in cal), and columns D, E and F contain their 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). 2 26 121 Food Items Hamburger McLean Big Mac Small FF Chicken Honey Chef Salad Garden Salad Egg McMutin Wheaties Yogurt Milk Orange Grapefr. Apple . Helle882 6 BCDEFGHIJKLM Price Calorie Prot. Fat Sod.A C B1 B2 Nia. Calc Iron cal. 8. 3. mg. RDA 0.59 265 129 490442010201015 1.79 320 22 10 67010 1.65 S001 89061 0.68 2201 11001 1.56 2701 201 15 58001 45 01 0 0 2.69 170 171 400 1.96 50 1.36 28018 7101 1.09 9021 22020 0.63 10341 8021 0.3611092 130107 0.88 80101 01 01 1201 101 0.68 8000010042 0.68 90001 50 22 of 7 COLLE wola Care Me! 701 9 10 22908-98cool 12 13 14 15 Given that a "healthy" daily diet must contain, 1. at least 55 grams of protein; 2. at most 3000 milligrams of sodium; 3. at least 100% RDA of vitamin A; 4. at least 100% RDA of vitamin C; 5. at least 100% RDA of vitamin B1; 6. at least 100% RDA of vitamin B2; 7. at least 100% RDA of Niacin; 8. at least 100% RDA of Calcium; 9. at least 100% RDA of Iron; 10. no more than 30% of all calories should come from fat (1 g. of fat contains 9 cal. calories). Which food items and how many) should be selected for daily consumption, in order to optimize various objectives stated below, 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. SPRING 2020 IE 405 Big Mac Questions: 1. 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. 2. How valid is the continuity assumption in this real-life problem (according to continuity assumption, the decision variables can take non-integer values)? Comment on how the violation of this assumption can be handled. 3. Comment on ways to divide a "minimal cost" diet into three courses (breakfast, lunch and dinner) to generate "palatable and minimum cost" daily diets: come up with at least 5 constraints to generate palatable diets, e.g., Egg McMuffin or Wheaties can only be caten during breakfast, one order of French fries for each hamburger for lunch, no fries are caten during dinner. Hint: Decompose each singular variable xi, corresponding an individual food item i, into three variables (xil, xi2, xi3) corresponding to consumption levels at breakfast, noon and dinner, respectively. 4. Comment on how to deal with multiple objectives at the same time. Suppose that you want to minimize calorie intake and cost simultaneously. 5. (Bonus Question) Comment on how to achieve variety maximization instead of cost minimization). In order to model this scenario, you have to use integer variables