how to lose 40 pounds?

You are going to struggle with only 15 minutes a day but I would suggest some good cardio or weights if that is what you are going to allow yourself. 

I think more importantly you need to "make time" for yourself.  You are allowing the baby to be your excuse, you will not likely get there even if you try.  Housework and the baby need to be important but the baby has to take naps and when that happens, find 1/2 hour everyday to do some exercising.  If you allow yourself to make excuses as to why you "can't do something", you'll simply not do it.

You need to move a new thought to the forefront of your life and that is that you need to take care of yourself in order to properly care for your family.  If you don't, you will likely find yourself well beyond the 40 lbs. and feeling even more terrible.  The reason you feel terrible is because you are not healthy.  I've been there.  Get out and walk with the baby if you have to everyday for at least 30 minutes.  Remind yourself that you are doing this "for your baby" so that you are here many years from now for him/her.

Get going today.  A new you is just "

one pound ago

It is really hard to find energy to do anything when you don't get enough sleep but things will get better. When your baby is a teen, you will be up waiting for the teen's return from a evening with friends. In the meanwhile, put the baby in a stroller and walk while the baby is sleeping. Go to the library and get an exercise DVD and work out for 10 minutes every day. There are also exercise classes for new moms and babies in many communities. That would be good for you because you will meet other mothers. At seven months the baby should be old enough to stay near you while you do household chores so you can get somethings done around the house. I think your difficulty in exercising is in part due to being still overwhelmed by taking care of the baby and the house. It is hard, sometimes very lonely and I wonder if you like so many of us, tend to use food as a way of feeling better? Make yourself a large salad with chick peas, shredded carrots, dark leafy vegetables, hard boiled egg whites, tuna or turkey slices and whatever else you like in the morning. Then when you are hungry you will have something to eat rather than grabbing junk. Please write again and tell us how you are doing .