Calculus and vectors

A cylindrical tank is to have a capacity of 1000 m³. It is to fit into a foundry that is 12 m wide with a height of 11 m.

The base of the tank will cost half as much as the top. The metal for the side of the tank will cost four fifths as much as the top.

An equation that can be used to model the cost of the tank is C(r)=(3/2)pi r^2+(1600/r) . Determine any restrictions on r. You need not solve further.

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