minimization of a water tank
Thanks in advance, it's attached. In case you can't read it, the problem states: The tank below is to be constructed to hold 5.00 x 10^5L when filled completely. The shape is cylindrical with a hemispherical top. The cost is a function of surface area, it will cost $300/(m^2) for the cylindrical portion, and $400/(m^2) for the hemispherical portion. Ignore the cost to construct the bottom circular area.
Specify the dimensions, H & R which will result in the lowest dollar cost, where H is the height of the cylinder, and R is the radius of the sphere and of the cylinder.