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 40calories. 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 unitsof 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 requirementwith 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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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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Samantha has an exercise regimen at the local gym that includes using a treadmill, stair machine, and cycle. According to an exercise website, a 130-lbd person like Samantha will burn, on average, about 600 calories per hour running on a treadmill, about 500 calories per hour on the stair machine, and about 300 calories per hour on the sycle. Samantha wants to spend 9.5 hours a week in the gym, and would like to spend twice as much time on the stair machine as the cycle. She wants to burn 4600 calories a week at the gym. Is this possible? (a) Write the system of equations that describe the problem. Lett be the number of hours she spends on the treadmill, s be the number of hours she spends on the stair machine, and c be the number of hours she spends on the cycle. Make sure to use the variables from the drop down menu. Calories equation: Time equation: Machines equation: (b) Use an online calculator to solve the system of equations. Put your answer into context by entering the values…
As part of a weight reduction program, a man designs a monthly exercise program consisting of bicycling, jogging, and swimming. He would like to exercise at most 32 hours, devote at most 2 hours to swimming, and jog for no more than the total number of hours bicycling and swimming. The calories burned per hour by bicycling, jogging, and swimming are 200, 573, and 257, respectively. How many hours should be allotted to each activity to maximize the number of calories burned? If he loses 1 pound of weight for each 3,500 calories burned, how many pounds will he lose each month exercising? How many hours should be allotted to each activity to maximize the number of calories burned? hours for swimming hours for bicycling hours for jogging C
A store has three types of laptops (A, B, C). There are twice as many type A than type B. There are 20 fewer type A than type C. There are 320 laptops in total. How many laptops are there of each type?
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Alexander has set up a lemonade stand outside his house and sells small сups and large cups. Each small cup holds 10 ounces of lemonade and each large cup hold 20 ounces of lemonade. How many ounces of lemonade would be needed to make 20 and 30 large cups of lemonade? How many ounces of lemonade would be small cups needed to makes small cups and l large cups of lemonade? 20 small cups and 30 large cups: 800 DELL @ # $ % & 2 4 8. e y u a f C V
As part of a weight reduction program, a man designs a monthly exercise program consisting of bicycling, jogging, and swimming. He would like to exercise at most 36 hours, devote at most 4 hours to swimming, and jog for no more than the total number of hours bicycling and swimming. The calories burned by this person per hour by bicycling, jogging, and swimming are 200, 694, and 256, respectively. How many hours should be allotted to each activity to maximize the number of calories burned? What is the maximum number of calories he will burn? (Hint: Write the constraint involving jogging in the form ≤0.) Let x, be the number of hours spent bicycling, let x₂ be the number of hours spent jogging, and let x3 be the number of hours spent swimming. What is the objective function? z = x₁ + x₂ + x3 22/11
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Bottled water and medical supplies are to be shipped to survivors ofan earthquake by plane. Each container of bottled water will serve 10 people and eachmedical kit will aid 6 people. Each plane can carry no more than 80,000 pounds. The bottledwater weighs 20 pounds per container and each medical kit weighs 10 pounds. Each planecan carry a total volume of supplies that does not exceed 6000 cubic feet. Each waterbottle is 1 cubic foot and each medical kit also has a volume of 1 cubic foot. Thus, the maximum value of z is 36000 and this occurs when x = 0and y = 6000.In practical terms, this means that the maximum number of earthquake survivors whocan be helped with each plane shipment is 36000. This can be accomplished bysending 6000 medical kits.A) TrueB) False

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