Problem 4: Linear Optimization You are the nutritionist in charge of designing Mr. Lebowski's weekly diet. The client's diet is constrained to consist of food items 1 through 5, and the next table provides information about the calorie amount, grams of protein, fat, and sugar per unit of food, as well as the client's preference rating (how much Mr. Lebowski likes each food). Sugar (grams/unit) Calories (per unit) 450 Protein Cerams/unit) 1.5 Fat Igrams/unit) 20.1 Preference Rating (per unit) 8.7 3.5 4 310 8.3 15 2.1 03 5.9 25 Food item 1 Food item 2 (meat) Food item 3 (meat) Food item 4 Food item 5 780 124 2.1 45 20 2.6 4 1.2 10 5 710 You also know that Mr. Lebowski's diet must satisfy some specific requirements. In particular: (1) The client has to consume at least 15 grams of protein on Monday, Wednesday, Friday, and Sunday and at least 30 grams of protein on the days the client exercises, ie., Tuesday, Thursday, and Saturday. (ii) The client has to consume at most 55 grams of fat on each day of the week. (10 points) Formulate a linear optimization problem to find the amount of each food that Mr. Lebowski should have in each day of the week, so that the amount of calories consumed is minimized. For each of the following parts, modify the original model developed in part 1. so as to incorporate the new requirements. a. (2 points) The client wants to consume at least 10 grams of sugar (in total) over the weekend. For example, consuming 6 grams of sugar on Saturday and 4.3 grams of sugar on Sunday satisfies this requirement. b. (2 points) The client wants to consume at least 1.2 units of food 1 (in total) over the three days he exercises (Tuesday, Thursday, and Saturday). For example, consuming 0.4 units of food 1 on Tuesday, 0 units on Thursday, and 0.9 units on Saturday satisfy this requirement