1. (A Diet Problem) Usually, one wants to minimize the amount of money spent on food. At the same time, one needs to maintain a certain level of nutrition. For males ages 19-30, the United States National Institute for Health recommends 3.7 liters of water per day, 1,000 milligrams of calcium per day, 90 milligrams of vitamin C per day, etc. So, one should address a "diet problem" one way or another In this regard, the following problem is a simple instance of a linear programming problem known in the literature as the "diet problem". Suppose that a dietician is preparing a diet consisting of two foods, A and B. Each unit of food A contains 20 grams of protein, 12 grams of fat, and 30 grams of carbohydrate, and costs 60 cents. Each unit of food B contains 30 grams of protein, 6 grams of fat, and 15 grams of carbohydrate, and costs 40 cents. The diet meal package being prepared must contain the following minimum requirements: at least 50 grams of protein, at least 24 grams of fat, and at least 30 grams of carbohydrate. (a) Use a linear programming formulation to represent formulate the problem of deciding how many units of foods A and B should be used in the diet meal package so that all of the minimal requirements are satisfied, and at the same time have a diet meal package whose cost is minimal. (b) Try to solve the diet problem that you have formulated in (a) using any methods that you know. (c) Briefly indicate what a practical real-world instance of this diet problem may look like