You have recently been hired by a hospital to provide advice on proper meal plans. Suppose we have three possible meals: a chicken dish, a beef dish, and a vegetarian dish. The chicken dish has 10 grams of fat and 600 calories. The beef dish has 22 grams of fat and 900 calories. The vegetarian dish has 4 grams of fat and 500 calories. A. We define our variables to be the number of each meal a person can eat in a day. We will allow for the possibility of fractional meals. After constructing a system of linear equations for the dietary constraints given, solve the system and describe the solution set. If there is more than one solution, state any limitations on the value(s) of free variables (remember that negative meal quantities are not possible). B. Now that you have a solution to a system of linear equations, build from it a vector equation. What does this vector equation mean? What do the individual vectors mean? What do the scalar multipliers for each vector mean? C. Now let's think about the vector equation as a geometric representation. More specifically, you have something of the form a +a+3+3=b. Ignore the b vector for now and let's focus on the three x vectors. What is the span of these three vectors? Draw a 2D representation of these three vectors to help you support your argument. What conclusion can you make about the set of all b vectors locations that can be reached in R^2_2 Suppose we add an additional nutritional constraint: the meal plan should consist of 40 grams of protein. The chicken, beef, and vegetarian meals have 14 grams, 16 grams, and 4 grams, respectively. D. As in part A, set-up and solve the system. What is your conclusion?