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After taking a nutrition class, a big Annie’s® Mac and Cheese fan decides to improve the levels of protein and fiber in her favorite lunch by adding broccoli and canned chicken. The nutritional information for the foods referred to in this exercise are given in the table below.a. [M] If she wants to limit her lunch to 400 calories but get 30 g of protein and 10 g of fiber, what proportions of servings of Mac and Cheese, broccoli, and chicken should she use?b. [M] She found that there was too much broccoli in the proportions from part (a), so she decided to switch from classical Mac and Cheese to Annie’s® Whole Wheat Shells and White Cheddar. What proportions of servings of each food should she use to meet the same goals as in part (a)?

(a) 1.0 serving of Mac, 1.5 servings of Broccoli, 0.8 servings of Chicken(b) 1.1 serving of Shells, 0.9 servings of Broccoli, 1.0 servings of Chicken

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 10

Linear Models in Business, Science, and Engineering

Introduction to Matrices

Missouri State University

Baylor University

Idaho State University

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in problem. Three. We have a person which is big fan off ends, Mac and cheese. We decided to improve the levels of protein and fiber by adding broccoli and canned chicken. Toe the Meghan cheese in the problem. We have the information regarding American the cheese, the first servant, Percle Broccoli, which is the second servant. Chicken, the third servant and shells, the fourth servant. We have here the calories, protein Ingram's and Fiber Ingram's. In every servant we have here 217. 10 to 51 5.4, 5.2, 70 15 0. And finally you have four shells 260 lying and fight for this problem. We want to toe for party to use broccoli and can chicken added to mac and cheese to produce a launch that has 400 colorless and 30 g off proteins and 10 g off five. We can do this by mixing the third the 1st 3rd servants. The first servant will be X one multiplied boy. The first nutrition information of the first servant 270 10, and to plus the amount of the second servant multiply by its information. 51 5.4 5.2 plus exit three. Well, the boy boy 70 15 and zero. Then using any metrics program to solve this system, we can write the augmented metrics first augmented metrics to contains thes three victors. Besides this vector 270 10 to 51 5.45 point two, 17, 15, 0, 400 30 and 10. Using software, we can get it. The reduced patron form in that in the reduced its reform, we have one zero zero. And in this month we have Oh, boy, nine it 58 We have zero one 1.5 for 39 and we have here 00 one 4.7 It 70 And using back substitution. Starting from the third equation, you can get that exit three equals 4.787 Next to equals, 1.5 for 39 and x one equals almost one. And we can approximate the amounts. As for Mac and cheese, we use one making the cheese. We use one servant for broccoli. We use 1.5 servants and for candid chicken news. Oh, point it. Servant for both v off the problem. We were replaced Mecca and the cheese with shells. Not to use too much broccoli. Then we will have the same augmented metrics in the above need. Except for the first column will be repressed Boy. The fourth column. 260. 260 mine five. Then we have the second two columns as it is 51 boy 55.45 point two, 70 15 0. And the right hand. So it as it is, you want to get 400 calories that the grams of protein and 10 g of fight using any metrics software, you will get this metrics as a Nick Wavell int toe. One 00 one point one zero 10 four point plane zero zero one on. We have here one which stays. We will. He will use 1.1 Servant off shells. 0, 00.9. Servant off broccoli. Finally, one servant off candy check. And this is the final answer of work to be. And this is the final answer off body

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