Reference no: EM132299576

When I was working out several days a week, I decided to see how many calories I could burn during a 60-minute workout. I decided that I wanted to maximize my calories burned during my workout. Here is the info I found:

I found that I could burn an average of 17 calories per minute doing cardio. (CAR)

I can burn an average of 25 calories per set of Heavy Weight reps. (HWR)

Each set of HWR takes 3 minutes. (30 seconds to lift and 2:30 to rest)

I can burn 8 cals/set of Light Weight Reps. (LWR)

Each set of LWR takes 1 minute. (30 seconds to lift and 30 seconds to rest.)

My workout was best when I did a HWR followed by 1 or 2 LWR for each muscle group I worked out.

Problem

I want to maximize the amount of calories I burn in a 60-minute workout.

I will do some cardio (CAR), some Heavy Weight Reps (HWR) and some light weight Reps (LWR).

When I exercise, I work out 2 major muscle groups with 3 different exercises. So, I will do a minimum of 2 HWR 3 times (18 mins minimum). This is over 6 exercises. Each exercise will consist of 1 or more HWR sets and an equal or greater number of LWR sets. (Let’s make it easier and say, 1 HWR set plus 1-2 LWR sets per exercise.

I want to maximize my weight training so I will do at 1 to 2 LWR per HWR. HWR<=LWR

When I exercise, I might do 1 set of HWR and 2 Sets of LWR, and for another exercise, I will do 1 set of HWR and 1 set of LWR.

The number of LWR and HWR must be the same for each muscle group.

1) If I want to maximize my calories burned, what is my objective function?

2) What are my constraints? (I have at least 5)

3) What type of a problem is this? (Choose 1: Linear, Integer or Mixed Integer) and why do you think that?