lagrange multipliers

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A cylindrical oil-storage tank is to be constructed for which the following costs apply:
cost per square meter metal for ides $30.00
combined costs of concrete base and metal bottom $37.50(cost per square meter)

top 7.50 (cost per square meter)


The tank is to be constructed with dimensions such that the cost is minimum for whatever capacity is selected.
a) One possible approach to selecting the capacity is to build the tank large enough for an additional cubic meter of capacity to cost $8.(note that this does not mean $8 per cubic meter average for the entire tank.) what is the optimal diameter and optimal height of the tank?
b) instead of the approach used in part(a), the tank is to be of such a size that the cost will be $9 per cubic meter average for the entire storage capacity of the tank. set up the lagrange multiplier equations and verify that they are satisfied by an optimal diameter of 20 m and optimal height of 15m.

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