A soup can of volume 500cm^3 is to be constructed.
The material for the top costs 0.4cents/cm^2 wwhile the material for the bottom and sides costs 0.2cents/cm^2. Find the dimensions that will minimize the cost of producing the can.
A soup can of volume 500cm^3 is to be constructed.
The material for the top costs 0.4cents/cm^2 wwhile the material for the bottom and sides costs 0.2cents/cm^2. Find the dimensions that will minimize the cost of producing the can.
You have two equations to consider:
V = πr^2h,
SA = 2πrh(side) + πr^2 (top) + πr^2(bottom)
thus: 500 = πr^2h, h = 500/(πr^2)
SA = 2πr(500/(πr^2) + πr^2 + πr^2
SA(including cost) = 0.4[2πr(500/(πr^2)] + 0.4[πr^2] + 0.2[πr^2]
I think now you find the derivative which should tell you what r is, and then plug in to find the dimensions.