Asked by jonh
                A cylinder shaped can needs to be constructed to hold 400 cubic centimeters of soup. The material for the sides of the can costs 0.03 cents per square centimeter. The material for the top and bottom of the can need to be thicker, and costs 0.06 cents per square centimeter. Find the dimensions for the can that will minimize production cost.
            
            
        Answers
                    Answered by
            Reiny
            
    let the radius be r
let the height be h
Volume = πr^2h
πr^2h = 400
h = 400/(πr^2)
cost = different prices x surface areas
= .03(2πrh) + 2(.06) πr^2
= .03[2πr(400/πr^2) + 4πr^2]
= .03[ 800/r + 4πr^2]
d(cost)/dr = .03[ -800/r^2 + 8πr] = 0 for a min of cost
800/r^2 = 8πr
100/π = r^3
r = 3.169
h = 400/(π(3.169)^2) = 12.679
check my arithmetic
    
let the height be h
Volume = πr^2h
πr^2h = 400
h = 400/(πr^2)
cost = different prices x surface areas
= .03(2πrh) + 2(.06) πr^2
= .03[2πr(400/πr^2) + 4πr^2]
= .03[ 800/r + 4πr^2]
d(cost)/dr = .03[ -800/r^2 + 8πr] = 0 for a min of cost
800/r^2 = 8πr
100/π = r^3
r = 3.169
h = 400/(π(3.169)^2) = 12.679
check my arithmetic
                    Answered by
            The Herald Of Cringe
            
    this be bottted
    
                                                    There are no AI answers yet. The ability to request AI answers is coming soon!
                                            
                Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.