A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply 1 unit of protein, 2 units of carbohydrates, and 1 unit of fat. Each ounce of nuts will supply 1unit of protein, 1 unit of carbohydrates, and 1 unit of fat. Every package must provide at least 8 units of protein, at least 12 units of carbohydrates, and no more than 11 units of fat.Let x equal the ounces of fruit and y equal the ounces of nuts to be used in each package.a. Write a system of inequalities to express the conditions of the problem.b. Graph the feasible region of the system.a. Fill in the chart.ProteinCarbohydratesFatFruitunit(s) per ounceunit(s) per ounceunit(s) per ounceNutsunit(s) per ounceunit(s) per ounceunit(s) per ounce..Requirements perpackageAt leastAt leastNo more thanunit(s)unit(s)unit(s)

Each ounce of fruit will supply 1 unit of protein, 2 unit of carbohydrate , 1 unit of fat Each ounce…

Answered: A dietician is planning a snack package…

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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A patient takes vitamin pills. Each day he must have at least 540 IU of vitamin A, 35 mg of vitamin B, and 80 mg of vitamin C. He can choose between pill 1, which contains 180 IU of vitamin A, 5 mg of vitamin B , and 10 mg of vitamin C, and pill 2, which contains 60 IU of vitamin A, 5 mg of vitamin , and 20 mg of vitamin C. Pill 1 costs 30 cent , and pill 2 costs 15 cent . Complete parts a and b below. a. How many of each pill should he buy in order to minimize his cost? What is the minimum cost?He should buy _____ of pill 1 and ______of pill 2. The minimum cost is $________. b. For the solution in part a, the patient is receiving more than he needs of at least one vitamin. Identify that vitamin, and tell how much surplus he is receiving. He is receiving ____ IU of vitamin A, _____ mg of vitamin B, ______ mg of vitamin c more than he needs
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A bakery produces cakes, doughnuts and muffins. Each cake requires 30 kg of flour, 21 kg of sugar and 12 kg of butter. Each doughnut requires 14, 12 and 6 kilograms of three ingredients, respectively. Finally, each muffin requires 8, 6 and 4 kilograms of these ingredients, respectively. Putting this information into table form, we get: Q10 Flour Sugar Butter Cakes 30 21 12 Doughnuts 14 12 Muffins 4 Supplies of these ingredients vary from day to day, so the bakery needs to determine a different production run each day. If 480 kg of flour, 360 kg of sugar and 200 kg of butter are available, find the number of cakes, doughnuts and muffins to be baked that day using all suitable numerical methods. You have to explain the chosen of the method and why the other method cannot be used. Check your exact answer using scientific calculator or inverse matrix method In Microsoft Excel.
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A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply zero units of protein, 3 units of carbohydrates, and 2 units of fat, and will contain 40 calories. Each ounce of nuts will supply 3 units of protein, 1 unit of carbohydrate, and 4 units of fat, and will contain 50 calories. Every package must provide at least 3 units of protein, at least 7 units of carbohydrates, and no more than 12 units of fat. Find the number of ounces of fruit and number of ounces of nuts that will meet the requirement with the least number of calories. What is the least number of calories? Let x be the ounces of fruit and y be the ounces of nuts. What is the objective function that must by minimized?

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