Problem SolvingA. The nutritionist of CMU Hospital serves lunch consisting of two courses, A and B.Assume each unit of A has 6 grams of fat, 6 grams of carbohydrates and 18 grams ofprotein whereas each unit of B has 8 grams of fat, 4 grams of carbohydrates and 24grams of protein. If the nutritionist wants to provide the patients no more than 40 grams offat, no more than 28 grams of carbohydrates, how many units of A and B should beserved to maximize the amount of protein?Required:1) Formulate the linear programming model

The linear function that needs to be optimized(maximize or minimize) is called the objective…

Answered: The nutritionist of CMU Hospital serves…

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter11: Systems Of Equations

Section11.CT: Test

Problem 24CT

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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.
A Toot can be made in 30 minutes and has a feather attached to it. A Wheet requires 15 minutes, has two feathers, and is sprinkled with 0.5 oz of sequin powder. A Honk requires 30 minutes, has three feathers, and one oz. of sequin powder. The net profit is $0.40 per Toot, $0.50 per Wheet, and $0.80 per Honk. The following resources are available: 80 hrs of labor, 360 feathers, and 90 oz. of sequin powder. Determine the quantity of each type of noisemaker that maximizes profit.
A Toot can be made in 30 minutes and has a feather attached to it. A Wheet requires 15 minutes, has two feathers, and is sprinkled with 0.5 oz of sequin powder. A Honk requires 30 minutes, has three feathers, and one oz. of sequin powder. The net profit is $0.40 per Toot, $0.50 per Wheet, and $0.80 per Honk. The following resources are available: 4800 minutes of labor, 360 feathers, and 90 oz. of sequin powder. Determine the quantity of each type of noisemaker that maximizes profit.
Select 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.
The nutrition club serves a luncheon consisting of two dishes: A and B. Assume each unit of dish A has 4grams of fat, 4grams of carbohydrates and 16grams of protein, whereas each unit of dish B has 8grams of fat, 4grams of carbohydrates and 24grams of protein. If the nutritionist planning the luncheon want to provide no more than 40grams of fat, no more than 28grams of carbohydrates, how many units of dish A and dish B should be served to maximize the amount of protein? solve using the graphical method.
A diesel engine uses Type A filter and high-grade lubricating oil costing P5.50 per liter. With this filter, the oil and the filter have to be changed every 500 hours of operation, and 5 liters of coil have to be added every 100 hours. This filter costs P148 a piece. Eighty liters of coil fill the engine. Another type, filter B, costing P120 may be used with a lower grade of oil costing P4.80 per liter. However, if this filter is used, the oil and filter have to be changed every 300 hours, and 10 liters are added after each 150 hours the engine is used. Which type of filter and oil would you recommend?
A gymnast wishes to get certain amounts of nutrients from her breakfast cereals. She has the choice of either eating puffs or flakes or a mix of the two. From the breakfast she should obtain at least 2 mg of thiamine, 4 mg of niacin, and 500 cal. One ounces of puffs has 0.3 mg of thiamin, 3 mg of niacin, and 100 cal; One ounce of flakes has 0.1 mg of thiamine, 0.05 mg of niacin and 150 cal. One ounce of puff costs 5 cents and one ounce of flakes cost 3 cents. Formulate a linear programming solution.
A high school dietician is planning menus for the upcoming month. Anew item will be spaghetti with sauce. The dietician wants each serving tocontain at least 10 grams of protein and at least 40 grams of carbohydrates.Spaghetti contains 5 grams of protein and 32 grams of carbohydrates per cup,and the sauce contains 4 grams of protein and 5 grams of carbohydrates percup. For aesthetic reasons, the dietician wants a ratio of spaghetti to sauce to be4:1.Spaghetti costs $0.30 per cup to buy and prepare, and the sauce $0.40 per cupto buy and prepare. The dietician wants to minimize the cost per serving andkeep the calories per serving 330 or less. The sauce contains 100 calories percup, and spaghetti contains 160 calories per cup.Formulate a linear programming model for this problem.
1.Dennis wants to use cottage cheese and yogurt to increase the amount of protein and calcium inhis daily diet. An ounce of cottage cheese contains 3 grams of protein and 15 milligrams ofcalcium. An ounce of yogurt contains 1 gram of protein and 41 milligrams of calcium.How many ounces of cottage cheese and yogurt should Dennis eat each day to provide exactly 62grams of protein and 760 milligrams of calcium?
parts a and b plewse
A campus student group is raising funds for charity by selling cups of boba tea. The expenses incurred by this student group are the cost of materials, estimated at $2 per cup (tea, boba, milk, sugar, cups, the big honking straws, napkins, etc.) and the $150 cost of renting the brewing and cooking space. The group will charge students $4 for each cup.a. Write down the associated cost, revenue, and profit functions. b. How many cups of boba must they sell to break even?c. What profit (or loss) results from the sale of 50 cups?
A company makes three components for sale. The components are processed on two machines: a shaper and a grinder. The time required. (in minutes) on each machine are as follows: Component Shaper Time Grinder Time A 6 4 B 4 5 C 4 2 The shaper is available for 7200 min. and grinder for 6600 min. No more than 200 units of component C can be sold, but up to 1000 units of each of the other components can be sold. In fact the company has orders for 600 units of component A that must be satisfied. The profit contributions for components A, B and C are $8, $6 and $9 respectively. Formulate the problem for deciding the production quantities. Solve the problem using Excel Solver. Run the sensitivity analysis report in Excel Solver. What are the objective coefficient ranges (Range of Optimality) for each coefficient. Interpret these. What are the dual prices for each constraint? Interpret these. What are the right-hand side ranges (Range of Feasibility)? Interpret them. If more time is…

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