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Nutrition Information per Serving Nutrient Mac and Cheese Broccoli Chicken Calories 70 Protein (g) 15 Fiber (g) 0 270 10 2 51 5.4 5.2 Shells 260 9 5

Nutrition Information per Serving Nutrient Mac and Cheese Broccoli Chicken Calories 70 Protein (g) 15 Fiber (g) 0 270 10 2 51 5.4 5.2 Shells 260 9 5

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1.10 Exercises 1. The container of a breakfast cereal usually lists the number of calories and the amounts of protein, carbohydrate, and fat contained in one serving of the cereal. The amounts for two common cereals are given below. Suppose a mixture of these two cereals is to be prepared that contains exactly 295 calories, 9 g of protein, 48 g of carbohydrate, and 8 g of fat. a. Set up a vector equation for this problem. Include a state- ment of what the variables in your equation represent. b. Write an equivalent matrix equation, and then determine if the desired mixture of the two cereals can be prepared. Nutrition Information per Serving General Mills Cheerios Nutrient Calories Protein (g) Carbohydrate (g) Fat (g) 4 20 Quaker 100% Natural Cereal 130 3 18 5 V 2. One serving of Post Shredded Wheat supplies 160 calories. 5 g of protein, 6 g of fiber, and 1 g of fat. One serving of Crispix supplies 110 calories, 2 g of protein, .1 g of fiber. and .4 g of fat. a. Set up a matrix B and a vector u such that Bu gives the amounts of calories, protein, fiber, and fat contained in a mixture of three servings of Shredded Wheat and two servings of Crispix. Tb. Suppose that you want a cereal with more fiber than Crispix but fewer calories than Shredded Wheat. Is it possible for a mixture of the two cercals to supply 130 calories, 3.20 g of protein, 2.46 g of fiber, and .64 g of fat? If so, what is the mixture" 3. 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 are given in the table. 2- Nutrition Information per Serving Nutrient Calories Protein (g) Fiber (g) Mac and Cheese Broccoli Chicken Shells 260 51 5.4 9 5.2 5 270 10 2 15 0 Ta. 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? propor- Tb. She found that there was too much broccoli in the tions 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)? 4. The Cambridge Diet supplies 8 g of calcium per day, in addition to the nutrients listed in Table 1 for Example 1. The amounts of calcium per unit (100 g) supplied by the three ingredients in the Cambridge Diet are as follows: 1,26 g from nonfat milk, .19 g from soy flour, and .8 g from whey. Another ingredient in the diet mixture is isolated soy protein, which provides the following nutrients in each unit: 80 g of protein, 0 g of carbohydrate, 3.4 g of fat, and 18 g of calcium. a. Set up a matrix equation whose solution determines the amounts of nonfat milk, soy flour, whey, and isolated soy protein necessary to supply the precise amounts of protein, carbohydrate, fat, and calcium in the Cam- bridge Diet. State what the variables in the equation represent. Tb. Solve the equation in (a) and discuss your answer. T In Exercises 5-8, write a matrix equation that determines the loop currents. If MATLAB or another matrix program is available. solve the system for the loop currents.
Transcribed Image Text:1.10 Exercises 1. The container of a breakfast cereal usually lists the number of calories and the amounts of protein, carbohydrate, and fat contained in one serving of the cereal. The amounts for two common cereals are given below. Suppose a mixture of these two cereals is to be prepared that contains exactly 295 calories, 9 g of protein, 48 g of carbohydrate, and 8 g of fat. a. Set up a vector equation for this problem. Include a state- ment of what the variables in your equation represent. b. Write an equivalent matrix equation, and then determine if the desired mixture of the two cereals can be prepared. Nutrition Information per Serving General Mills Cheerios Nutrient Calories Protein (g) Carbohydrate (g) Fat (g) 4 20 Quaker 100% Natural Cereal 130 3 18 5 V 2. One serving of Post Shredded Wheat supplies 160 calories. 5 g of protein, 6 g of fiber, and 1 g of fat. One serving of Crispix supplies 110 calories, 2 g of protein, .1 g of fiber. and .4 g of fat. a. Set up a matrix B and a vector u such that Bu gives the amounts of calories, protein, fiber, and fat contained in a mixture of three servings of Shredded Wheat and two servings of Crispix. Tb. Suppose that you want a cereal with more fiber than Crispix but fewer calories than Shredded Wheat. Is it possible for a mixture of the two cercals to supply 130 calories, 3.20 g of protein, 2.46 g of fiber, and .64 g of fat? If so, what is the mixture" 3. 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 are given in the table. 2- Nutrition Information per Serving Nutrient Calories Protein (g) Fiber (g) Mac and Cheese Broccoli Chicken Shells 260 51 5.4 9 5.2 5 270 10 2 15 0 Ta. 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? propor- Tb. She found that there was too much broccoli in the tions 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)? 4. The Cambridge Diet supplies 8 g of calcium per day, in addition to the nutrients listed in Table 1 for Example 1. The amounts of calcium per unit (100 g) supplied by the three ingredients in the Cambridge Diet are as follows: 1,26 g from nonfat milk, .19 g from soy flour, and .8 g from whey. Another ingredient in the diet mixture is isolated soy protein, which provides the following nutrients in each unit: 80 g of protein, 0 g of carbohydrate, 3.4 g of fat, and 18 g of calcium. a. Set up a matrix equation whose solution determines the amounts of nonfat milk, soy flour, whey, and isolated soy protein necessary to supply the precise amounts of protein, carbohydrate, fat, and calcium in the Cam- bridge Diet. State what the variables in the equation represent. Tb. Solve the equation in (a) and discuss your answer. T In Exercises 5-8, write a matrix equation that determines the loop currents. If MATLAB or another matrix program is available. solve the system for the loop currents.
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