Optimisation - Rainwater Tank

#anon

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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.
 

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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.

12000 litre = 12 m^3

You cannot have the tank to be 2 m radius and 3 m tall - with the given constraint on the volume.

Volume of that cylinder (that you have drawn) is V = π * 4 * 3 m^3 >> 12 m^3

You have to have those as variables: "r" (≤ 2)

and

h = 12/(π*r^2) where h ≤ 3

Now write your cost function in terms of these variables.
 
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