A large rectangular container of volume 160 cubic metres is to be made out of different materials to achieve a base which is stronger that the top, which in turn is stronger than the sides. The material for the base costs $15 per square metre, the material for the top costs $10 per square metre, and the material for the sides costs $5 per square metre. What dimensions should the container have so that the cost is minimised, and what is the minimum cost?

Question

anonymous · Answer

I understand I need to write a PDE to satisfy the above problem, but I'm unsure how to go about it.

dumbcow · Answer

define cost as area of each side * price
dimensions are l,w,h

cost = 25lw +10lh +10wh
then use volume = lwh = 160  --> h = 160/lw
substitute in

cost = 25lw + 1600/w + 1600/l
take partial derivatives and set equal to 0
solve system for l and w

dumbcow · Answer

if want the solution, i can give it to you

anonymous · Answer

Perfect. Thank you.