Task 2: Linear Programming Imagine you are trying to maximize the calories you burn in a 60-minute workout you do a few times a week. Running burns 9 calories per minute, aerobics burns 6 calories per minute, and rowing burns 7 calories per minute. You want to perform all three exercises to work different muscle groups. For the best effect, you need to run for at least 5 minutes and row for at least 15 minutes. And your aerobics session should be no more than 30 minutes. How many minutes should you perform each exercise to burn the maximum calories? a. Write a system of inequalities based on the given constraints. Then note the objective function. Type your response here: b. Convert the inequalities into equations, and then use the substitution method to find four possible vertices in the form (x, y, z). Type your response here: c. Test the four possible vertices that you found in the objective function in part a. Use those values to determine which set of values maximizes the objective function. Type your response here:
Task 2: Linear Programming Imagine you are trying to maximize the calories you burn in a 60-minute workout you do a few times a week. Running burns 9 calories per minute, aerobics burns 6 calories per minute, and rowing burns 7 calories per minute. You want to perform all three exercises to work different muscle groups. For the best effect, you need to run for at least 5 minutes and row for at least 15 minutes. And your aerobics session should be no more than 30 minutes. How many minutes should you perform each exercise to burn the maximum calories? a. Write a system of inequalities based on the given constraints. Then note the objective function. Type your response here: b. Convert the inequalities into equations, and then use the substitution method to find four possible vertices in the form (x, y, z). Type your response here: c. Test the four possible vertices that you found in the objective function in part a. Use those values to determine which set of values maximizes the objective function. Type your response here:
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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Transcribed Image Text:Task 2: Linear Programming
Imagine you are trying to maximize the calories you burn in a 60-minute workout you do a
few times a week. Running burns 9 calories per minute, aerobics burns 6 calories per minute,
and rowing burns 7 calories per minute. You want to perform all three exercises to work
different muscle groups. For the best effect, you need to run for at least 5 minutes and row for
at least 15 minutes. And your aerobics session should be no more than 30 minutes. How
many minutes should you perform each exercise to burn the maximum calories?
a. Write a system of inequalities based on the given constraints. Then note the objective
function.
Type your response here:
b. Convert the inequalities into equations, and then use the substitution method to find four
possible vertices in the form (x, y, z).
Type your response here:
c. Test the four possible vertices that you found in the objective function in part a. Use those
values to determine which set of values maximizes the objective function.
Type your response here:
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