There are many studies showing that a 30 minutes workout is good for everyone. There is also tones of evidence supporting the fact that eating healthy food and having a proper diet is good for both physical and mental health. I also encourage you to read this article about 10 steps to a better brain published in the newscientist to see what else is necessary for you.
It is also important to control our diet after a short (daily) workout. Here is some advice taken from here . To summarize briefly; take up as much as half the calorie you burned during exercise. The intake calorie should be spend roughly as 60% carbs, 25% protein, and 15% fat. Finally, drink about 16-20 ounces of water after workout. The ideal time to eat after a workout is within 30 minutes to two hours.