calculus, maximum minimum

Question

A cylindrical container with no top is to be constructed for a fixed amount of money. The cost of material for the bottom is Php 3 per square inch, and the cost of material for the lateral surface is Php 2 per square inch. Find the relationship between the radius and height of the container having the greatest volume

Answer 1

So Nicholas S.,

What are you waiting for? Write an equation for the cost of the jar, and an equation for the volume of the jar as a function of radius and height. If F is the fixed cost, use the first equation to express h as f(F,r). Then use that function in the second equation (for the variable h) to express V as f(F,r). At maximal volume, dV/dr = 0, doesn't it. So what are you waiting for? Write it, solve it!

And don't get caught with your hand in it, if it is to be a "cookie jar"?

-- Cheers, --Mr. d.