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: