Calculus Maximum and Minimum: open rectanglar tank to have vol. 144m^3; edges of sides in 3:1 ratio; show that cost is...

[reggiwilliams]

Having trouble with this question Had a go and made minimum dimensions 12 x 4 x 3. The height being 3.
I’m presumably missing something.
Can you help

 

[khansaheb]

I’m presumably missing something.

You would have to share your work to catch whatever you are missing..

 

[reggiwilliams]

Here are my workings

 

[BigBeachBanana]

Here are my workings

They told you the depth h = 1 meter. Am I missing something?

 

[reggiwilliams]

Exactly but my calculations show least size of tank is 12x4x3 a height of 3 so not sure how you get to height of 1

 

[skeeter]

cost of the lead lining is proportional to the surface area of the open container

if h = 3, then A = 144

if h = 1, then the area of the bottom alone is 144 … adding the area of the sides would make A > 144

I’d say you are correct.

 

[BigBeachBanana]

Exactly but my calculations show least size of tank is 12x4x3 a height of 3 so not sure how you get to height of 1

Misread the problem statement. I'd agree with @skeeter above.