This can be done using the category system. However, this calendar will allow you to display everyone using a single calendar. Then by adding the filter plugin, your visitors can filter down to a single tutor at a time.
This may simplify your layout.
Feel free to download the V6 demo and have a crack at it. You'll have 7 days with the demo.
Or your can purchase the V7, and then you have a trial period where you can ask for a refund.
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