A factory produces a closed rectangular parallelepiped vats having the capacity of 10 cubic meters. Find the dimensions that will make the cost of the lining a minimum?
The volume of a rectangular parallelepiped is "xyz" which is 10 cubic meters
The surface area of the figure is "2xy+2xz+2yz" which is to be minimized.
Using Langrage method.
Equating the partial derivatives to zero.
Solving (1) and (2) together, we have that;
Also, solving (2) and (3) together, we have that;
Thus,
Substituting this into (4), we have that;
Hence the dimension to minimize the lining is
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