Low cost, long battery life, with DVD drive

I am looking for a low cost laptop to run various linux distros on No gaming, mainly web surfing and learning how to use and operate linux. Here are the bullet points I am looking for

1: Low Cost (Less than $300 preferred $500 Max)

2: Long Battery Life

3: DVD drive

4: 1080 screen

5: Screen size 11-13"

6: WiFi card (Would prefer to have AC/N)

Smaller, thinner and lighter is better for ease of travel.

Will be bought in USA I don't care about hard drive size, or brand.

Thanks for your suggestions.