Question

It's been a while since I've done Optimization problems. if someone can help me remember how to do this problem, I would appreciate it. http://i.imgur.com/nktFO.png

Answer 1

A = 4(pi)r^2 + 2(pi)(r)(h) C(ost) = 8(pi)r^2 + 2(pi)(r)(h)

V = (4/3)(pi)r^3 + (pi)(r^2)(h) = 6600

h = [6600 - (4/3)(pi)r^3]/[(pi)r^2]

C = 8(pi)r^2 + 2[6600 - (4/3)(pi)r^3]/r

Now, differentiate C(ost) with respect to "r" for critical values. The rest is easy.

Answer 2

Once you get your value for "r", you can then substitute that value into the equation defining "h" (3rd line in first post) to get "h".

Notes: 2 hemispheres = 1 sphere, so 4(pi)r^2 was used as the first term in defining "A". Twice the "sphere" material for cost. The "sides" is not not multiplied by 2 in determining cost.

Are you able to perform differentiation now that the equations are set up?

Answer 3

yes I can. I definitely think the hardest part is setting it up. thanks a lot! If I can't figure it out, I'll send you a message :D

Answer 4

Yes, you are right. Setting it up is hardest. I suggest you go over my equations just to see if I made any mistake. I offer the equations, not so much as a solution (though you are welcome to that), but so that you can follow someone's thinking and correct it if need be. If you confirm the equations, then they're right, but I'm pretty sure they are anyway. Good luck to you in all of your studies and thx for the recognition! Nice working with you. @christopherklug999