What is the minimum number of hours of exercise that she can do?

[pupli]

A physical fitness enthusiast decides to devote her exercise time to a combination of jogging and
cycling. She wants to earn aerobic points (a measure of the benefit of the exercise to strengthening
the heart and lungs) and also to achieve relaxation and enjoyment. She jogs at 6 miles per hour
and cycles at 18 miles per hour. An hour of jogging earns 12 aerobic points and an hour of cycling
earns 9 points. Each week she would like to earn at least 36 aerobic points, cover at least 54 miles,
and cycle at least as much as she jogs. What is the minimum number of hours of exercise that she
can do in order to satisfy her requirements


its a linear programming problem btw

 

[stapel]

A physical fitness enthusiast decides to devote her exercise time to a combination of jogging and
cycling. She wants to earn aerobic points (a measure of the benefit of the exercise to strengthening
the heart and lungs) and also to achieve relaxation and enjoyment. She jogs at 6 miles per hour
and cycles at 18 miles per hour. An hour of jogging earns 12 aerobic points and an hour of cycling
earns 9 points. Each week she would like to earn at least 36 aerobic points, cover at least 54 miles,
and cycle at least as much as she jogs. What is the minimum number of hours of exercise that she
can do in order to satisfy her requirements


its a linear programming problem btw

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

Please be complete, starting with the variables you picked and your definitions for each. Thank you!

 

[pupli]

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

Please be complete, starting with the variables you picked and your definitions for each. Thank you!

i havent started i cant start its just so confusing pls

 

[pupli]

im soo tired i can never get math it makes me sick

 

[JeffM]

im soo tired i can never get math it makes me sick

In EVERY word problem from basic algebra on, the first step ALWAYS is to WRITE down what are the relevant variables. and what symbol represents each variable.

Here is how you do this

c = hours cycling
j = hours jogging
h = hours exercising

Now that was not hard.

The second step ALWAYS is to translate the relevant quantitative information into mathematical form and WRITE them down. In the case of a programming problem, you are trying to optimize (either minimize or maximize) some variable.

In this problem you are trying to do what, minimize or maximize, to which variable, c, j, or h? Write it down. That's not hard either.

Moreover, in a programming problem, you are trying to optimize that variable subject to constraints. What are they in mathematical form? This may require a bit of work.

Hint: one of them is \(\displaystyle c \ge j.\) What are the other constraints?

Your third step is to solve what is now a purely mechanical math problem.