A company manufactures cylindrical metal drums with open tops with a volume of 2 cubic meters. The metal used to manufacture the drums cost $2 per square meter for the sides and $3 per square meter for the bottom. What should the dimensions be of the drums to minimize the cost of metal in their production? what is the ratio height/ radius?

The cost is minimized for

 and then and the ratio height / radius = 2.3

Step-by-step explanation:

When you solve these kind of problems you always need to ask yourself what am I minimizing or maximizing, for this case you need to minimize the cost function.

Suppose that the bottom of your drum has a radius and a height and a height then the are of the circle at the bottom would be

And the area of the sides would be given by

According to what they say the cost of the sides is 2$ per square meter and the cost of the bottom is 3$ per square meter.

So the cost would be given by this function.

Cost =

But they mention that the volume = 2 cubic meters. On the other hand

Volume = = 2   if we replace on Cost we get that

When you find the derivative of that and equal to zero you will find that the the cost is minimized for

 and then and the ratio height / radius = 2.3

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step-by-step explanation:

9-15%

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

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