(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I need help on an optimization problem involving a hexagonal prism with no bottom or top, but the top is covered by a trihedral pyramid which has a displacement, x, such that the surface area of the object is at a minimum for a given volume. The assigned variables include:

A= the surface area of the object

a= the length of each side of the hexagon (a=1)

h= the height of the prism

x= displacement

2. Relevant equations

Given that A= 6(ah-1/2ax) + 3a[tex]\sqrt{3}[/tex]*[tex]\sqrt{x^2+(a^2/4)}[/tex], use calculus to find the displacement, x that yields the minimum surface area. Calculate x if a=1.

3. The attempt at a solution

I'm struggling trying to find a secondary equation for this optimization problem and I think I need to use an equation evolving h, but I'm not sure what.

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# Homework Help: Optimization: Minimum Surface Area

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