What is a good exercise workout that allows you to lose weight that consists of only Jumping Jacks Lunges Burpees Push-ups and Treadmill?

Short and tough (but not to tough) workouts are better than long ones. I would suggest starting with cardio, to warm up your body. You need to set a number of how many you want to start off with for each exercise, the following example is just an idea to start off and feel free to modify the numbers as you progress.

Here's an idea:

1 min walking on treadmill followed by 4 minutes of jogging.

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20 lunges each leg

20 burpees

50 jumping jack

20 push-ups

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*Repeat the designated section above twice*

4 minutes of jogging followed by 1 minute of walking (as a cool down)

You could also run between your two sets of the designated area exercises.

Don't forget to stretch before and after your workout.

Also drink water, but no too much water.

Hope this helped. :)