DIET PLANNING A nutritionist at the Medical Center has been asked to prepare a special diet for certain patients. She has decided that the meals are to be prepared from Foods A and B and that the meals should contain a mini-mum of 400 mg of calcium, 10 mg of iron, and 40 mg of vitamin C. Each ounce of Food A contains 30 mg of calcium, 1 mg of iron, 2 mg of vitamin C, and 2 mg of cholesterol. Each ounce of Food B contains 25 mg of calcium, 0.5 mg of iron, 5 mg of vitamin C, and 5 mg of cholesterol. How many ounces of each type of food should be used in a meal so that the cholesterol content is minimized and the minimum requirements of calcium, iron, and vitamin C are met?
Want to see the full answer?
Check out a sample textbook solutionChapter 3 Solutions
Finite Mathematics for the Managerial, Life, and Social Sciences, 11th Edition
- Cholesterol Cholesterol in human blood is necessary, but too much can lead to health problems. There are three main types of cholesterol: HDL (high-density lipoproteins), LDL (low-density lipoproteins), and VLDL (very low-density lipoproteins). HDL is considered “good” cholesterol; LDL and VLDL are considered “bad” cholesterol. A standard fasting cholesterol blood test measures total cholesterol, HDL cholesterol, and triglycerides. These numbers are used to estimate LDL and VLDL, which are difficult to measure directly. Your doctor recommends that your combined LDL/VLDL cholesterol level be less than 130 milligrams per deciliter, your HDL cholesterol level be at least 60 milligrams per deciliter, and your total cholesterol level be no more than 200 milligrams per deciliter. (a) Write a system of linear inequalities for the recommended cholesterol levels. Let x represent the HDL cholesterol level, and let y represent the combined LDL VLDL cholesterol level. (b) Graph the system of inequalities from part (a). Label any vertices of the solution region. (c) Is the following set of cholesterol levels within the recommendations? Explain. LDL/VLDL: 120 milligrams per deciliter HDL: 90 milligrams per deciliter Total: 210 milligrams per deciliter (d) Give an example of cholesterol levels in which the LDL/VLDL cholesterol level is too high but the HDL cholesterol level is acceptable. (e) Another recommendation is that the ratio of total cholesterol to HDL cholesterol be less than 4 (that is, less than 4 to 1). Identify a point in the solution region from part (b) that meets this recommendation, and explain why it meets the recommendation.arrow_forwardA florist offers three sizes of flower arrangements containing roses, daisies, and chrysanthemums. Each small arrangement contains one rose, three daisies, and three chrysanthemums. Each medium arrangement contains two roses, four daisies, and six chrysanthemums. Each large arrangement contains four roses, eight daisies, and six chrysanthemums. One day, the florist noted that she used a total of 24 roses, 50 daisies, and 48 chrysanthemums in filling orders for these three types of arrangements. How many arrangements of each type did she make?arrow_forwardDiet Program Nicole started a new diet that requires each meal to have 460 calories, 6 g of fiber, and 11 g of fat. The table shows the fiber, fat, and Calorie content of one serving of each of three breakfast foods. How many servings of each food should Nicole eat to follow her diet!arrow_forward
- If a man has 4 sweaters and 5 pairs of slacks, how many different outfit can he wear?arrow_forwardA diet supplies 0.8 grams of calcium per day, in addition to the nutrients listed in the table to the right. The amounts of calcium per unit (100 g) supplied by the three ingredients in the diet are as follows: 1.25 g from nonfat milk, 0.18 g from soy flour, and 0.8 g from whey. Another ingredient in the diet mixture is isolated soy protein, which provides the following nutrients in each unit: 78 g of protein, 0 g of carbohydrate, 3.6 g of fat, and 0.15 g of calcium. Complete parts (a) and (b) below. 0.42 X₁ x2 X3 11 34 45 3 0.8 CIES X4 (Type an integer or decimal for each matrix element.) Amounts (g) Supplied per 100 Amounts (g) g of Ingredient Supplied by Diet in One Day a. Set up a matrix equation whose solution determines the amounts of nonfat milk, soy flour, whey, and isolated soy protein necessary to supply precise amounts of protein, carbohydrate, fat, and calcium in the diet. Nutrient Nonfat Soy Whey Milk flour 36 Protein Carbohydrate 52 0 Fat 50 14 33 75 7 1.2 34 45 3arrow_forwardThe Enormous State University Choral Society is planning its annual Song Festival, when it will serve three kinds of delicacies: granola treats, nutty granola treats, and nuttiest granola treats. The following table shows some of the ingredients required for a single serving of each delicacy, as well as the total amount of each ingredient available. Nuttiest Total Granola Nutty Granola Granola Available Toasted Oats 1 1 1,300 (ounces) Almonds 4 8. 8. 11,000 (ounces) Raisins 4 8 3,000 (ounces) The society makes a profit of $6 on each serving of granola, $8 on each serving of nutty granola, and $3 on each serving of nuttiest granola. Assuming that the Choral Society can sell all that it makes, how many servings of each will maximize profits? granola serving(s) | serving(s) | serving(s) nutty granola nuttiest granola How much of each ingredient will be left over? toasted oats ounce(s) almonds ounce(s) raisins ounce(s)arrow_forward
- The Big Bang Novelty Company makes three basic types of noisemakers: Toot, Wheet, and Honk. The respective selling prices are $0.9O, $0.75, and $1.25 per unit, respectively. Two Toots can be made per minute, and each one has a feather attached to it. Three Wheets can be made per minute; each one has two feathers and is sprinkled with one-half ounce of sequin powder. Four Honks can be made in a minute; each one has 3 feathers and one ounce of sequin powder. The manufacturing costs for Toots, Wheets, and Honks are $0.35, $0.40, and $0.50, respectively. The following resources are available: 80 hours of labor, 90 ounces of sequin powder, and 360 feathers. The management of Big Bang wants to produce at least three times as many Wheets as the combined total of Toots and Honks. How many units of each type of noisemaker should they make to maximize their total profit.arrow_forwardElizabeth wants to choose her day's menu from cereal, cheeseburgers, and french fries. However she must choose so that she gets at least 210 grams of carbohydrates, 20 grams of dietary fiber, and 80% of minimum daily requirements of vitamin A. The foods contain the following: Carbo- Calories hydrates Fiber Vitamin A Cereal 250 30 g 8 g 20% Cheeseburger 350 45 g 3 g 10% Fries 500 60 g 4 g How many of each food should she use in order to meet the restrictions and minimize calories? cereal cheeseburgers fries total calories Additional Materials M eBook Submit Answer G Search or type URL esc %24 4 %23 5 7 9 dele 2 3 Q W E S D F G H V B Marrow_forwardSelect the correct answer. A veterinarlan is mixing three different types of feed to produce a mixture that contains 44 grams of fat, 48 grams of carbohydrates, and 132 grams of protein. • Each serving of the first type of feed, x, contains 11 grams of fat, 24 grams of carbs, and 3 grams of protein. Each serving of the second type of feed, y, contains 4 grams of fat, 8 grams of carbs, and 31 grams of protein. • Each serving of the third type of feed, z, contains 10 grams of fat, 0 grams of carbs, and 18 grams of protein. Which matrix represents the system of equations that will give the number of servings of each type of feed the veterinarian should include? O A. 3 11 4 10 24 8 31 18 44 48 132 11 4 101 O B. 24 8 0 3 31 18 C. |組 O D. 4 10 44 24 8 0 48 3 31 18 132 All rights reserved.arrow_forward
- A food factory makes three types of cereals, A, B and C, from a mix of several ingredients: Oates, Apricots, Coconuts and Hazelnuts. The cereals are packaged in 2kg boxes. The following table provides details of the sales price per box of cereals and the production cost per ton (1000 kg) of cereals respectively. Sales price per box($) | Production cost per ton Cereal A 2.50 4.00 Cereal B Cereal C 2.00 2.80 3.50 3.00. The following table provides the purchase price per ton of ingredients and the maximum availability of the ingredients in tons respectively. |Ingredients Purchase price ($) per ton Maximum availability in tons Oates 100 10 Apricots Coconuts 120 80 Hazelnuts 200 2 The minimum daily demand (in boxes) for each cereal and the proportion of the Oates, Apricots, Coconut and Hazelnuts in each cereal is detailed in the following table, Proportion of Minimum demand (boxes) Oates | Apricots | Coconuts | Hazelnuts 0.05 Cereal A 1000 0.8 0.1 0.05 Cereal B Cereal C 700 0.65 0.2 0.05…arrow_forwardA doctor recommends that a patient take 100 mg each of niacin, riboflavin, and thiamin daily to alleviate a vitamin deficiency. In his medicine chest at home, the patient finds three brands of vitamin pills. The amounts of the relevant vitamins per pill are given in the table. How many pills of each type should he take every day to get 100 mg of each vitamin? Vitamax 3X pills Vitron pills VitaPlus pills VitaMax Vitron VitaPlus Niacin (mg) Riboflavin (mg) Thiamin (mg) 10 15 15 20 10 10 10arrow_forwardThe Enormous State University Choral Society is planning its annual Song Festival, when it will serve three kinds of delicacies: granola treats, nutty granola treats, and nuttiest granola treats. The following table shows some of the ingredients required for a single serving of each delicacy, as well as the total amount of each ingredient available. Total Granola Nutty Granola Granola Available Nuttiest Toasted Oats 1 1. 1,500 (ounces) Almonds (ounces) 4 8 8 14,000 Raisins 4 4,000 (ounces) The society makes a profit of $6 on each serving of granola, $8 on each serving of nutty granola, and $3 on each serving of nuttiest granola. Assuming that the Choral Society can sell all that it makes, how many servings of each will maximize profits? granola serving(s) nutty granola serving(s) nuttiest granola O serving(s) How much of each ingredient will be left over? toasted oats 0 ounce(s) almonds ounce(s) raisins 0 ounce(s)arrow_forward
- College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
- Algebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage