Thank you very much for the advice, I will put it to use and see how it works.
Your son sounds so normal. Count your blessings. He wants your companionship which is totally normal. If he did not want to be with you and wanted be alone in his room lining up toys, you would actually have a problem (such as autism). You do not have a problem. Be happy that you raised him in a way that he loves to be with you and wants your companionship. Give him something to entertain himself such a playclay or a puzzle and have him sit where he can see you cook or do homework. Enjoy him because there will be a day that he is grownup and does not need you anymore.
Yes, it is reasonable for him to do something when you are busy. Perhaps you can have him play with clay or draw things so that he can be near you but not engaged directly with you.
Maybe I didn't explain the situation as clearly as I should have. My son and I have quality time together we play games, color and go to the park. It is when I am making dinner or doing homework and I ask him to go play for a bit while I get these things done, that is when he throws his fits. He tells me that "playing is boring." He lacks the skills to entertain himself, for any amount of time. Is this normal behavior for a child of his age? Should I not expect him to be able to play by himself for 30 mins at his age?
There is no point in forcing him to be in his room to play. It is normal for young children to play by themselves some of the time and then go through stretches during which they want to have their parents' companionship. It sounds like your expectations for what is normal in a child of four need to be adjusted a bit.