Need doggie door, letting out AC

I love my dog more than anything, but jesus christ, he drives me insane sometimes. He’s super sweet and loving, but that also makes him incredibly needy. He hates to be away from me for even a moment, and prefers that I’m within sight at all times. As such, this spoiled brat comes with me everywhere, and that’s why he’s driving me nuts with this indoor-outdoor issue at home. He’s a natural guard dog, so he wants to go outside to check out the yard… but immediately wants to come back inside to make sure I’m still around. This means I’m either endlessly opening and closing the door for him, or I have to leave the door open entirely. As such, I’m spending hundreds of dollars to let my indoor air conditioning flow straight out into the summer heat every day. I can feel the rush of AC pass by me as it’s replaced by another push of hot and humid outdoor air coming inside. The entire area next to the door is continually about 15 degrees warmer than the rest of the house, and it’s right next to the thermostat so my central AC system cycled on and off endlessly. My energy bill has increased exponentially this summer since having to crank up the AC unit and letting my furry buddy out every five minutes. Now, every single time I go and fling open the outside door, I practically see dollar bills float out with the artificially cooled air. At this rate I don’t know what’s cheaper – to stop letting my dog out, to install a small doggie door, or to quit using AC entirely.

a/c plan