One easy to use tool to do so fairly automatedly is http://trimage.org/ (a free software front end to .jpg and .png compressing free software backends)
I also noticed there's one monster graphic (781 KB) on the front page of the blog ( https://blog.documentfoundation.org/ ), this file https://blog.documentfoundation.org/wp-content/uploads/2015/06/donatenow.png I suggest some manual operations: make the image size smaller, now it's 3000x3000 or so, enough to entirely fill the largest monitors available, twice. And I'm not convinced the colors should not be indexed, as it's basically "two color".
Fast websites make people happy. Ridiculously fast make people very happy. And not everybody in the world has a broadband connection.
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