Question

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? Write a system of inequalities based on the given constraints. Then note the objective function

Answer 1

Running burns the most calories folwed by aerobic

so max out the most and min the least


most running
running has no limit, so see least

aerobic, aerobic has to be at most 30 (less than 30)

rowing has to be at least 15 mins
say row=15 mins

then you have 45 mins left
max out on running (minus 1 tho to do running)

so
44mins running 1 min run, 15min row
total calories=507 calories burned

the way to do it is
x=running minutes
y=aerobic minutes
z=rowing minutes

x+y+z=60
9x+6y+7z=max calories
x≥5
y≤30
z≥15
those are the equations
not sure what the objective function is