Minimizing Surface Area/Volume

[Mldancer125]

Homework Statement

I need to find a solution to make a large capsule ( top and bottom are hemispheres and middle is a cyliner) The capsule must be big enough to hold .25 cubic meters of medicine. One hemisphere's materials costs $.0025 per square centimeter and the other hemisphere and cylinder materials costs $ .0015 per square centimeter. I need to know the optimal measurements to minimize the total materials cost for the case, as well as the total materials cost for this optimal design.

Homework Equations

V of sphere= 4/3pi r^3
V of cylinder= pi r^2h
SA of sphere=4 pi r^2
SA of cylinder= 2pi r^2+ 2pi rh

The Attempt at a Solution

 

[tiny-tim]

Welcome to PF!

Hi Mldancer125! Welcome to PF!

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