# A cylinder has a volume of 300 cubic inches. The top and bottom parts of the cylinder cost $2 per square inch. And the sides of the cylinder cost $6 per square inch. What are the dimensions of the Cylinder that minimize cost based on these constraints?

##### 1 Answer

The optimum dimensions are

#### Explanation:

We have to minimize the function

To get rid of one of the variables we use the fact, that the volume of the cylinder is given.

Now we can write

Now to find the value of

Now we have to find

Now we have to calculate

So finally we get the dimensions with the minimal price: