A 12,000 litre rainwater tank is to be built in the shape of a cylinder. It must be at most 3 metres tall, and have radius at most 2 metres. Its base costs 50 dollars per square metre, and the sides and top cost 30 per square metre. What are the cheapest and most expensive shapes that satisfy these conditions?
I need to find the total costs as a function of the height (H) and radius (R) and also the equation the connects the height (H) and radius (R).
I have come up with a diagram but do not know how to proceed next.
Any help would be appreciated. Thank you.