Answer:
r = 3.43 cm
h=18.94 cm
Step-by-step explanation:
The volume of the cylinder is:
where r is the radius of the circular base and h is the height of the cylinder.
The cost of the side of the cylinder is:
The cost ot the bottom of the container is:
The cost ot the top of the container is:
Then, the total cost of the container is:
From the volume, you could solve for one variable and substituting in the cost equation:
In order to minimize this fuction you need to calculate the derivative respect to r:
The critical points of the function are obtained when dC/dr=0:
To evaluate if this critical point is a minimum, you should get the second derivative:
For the critical point r = 3.43 cm, the second derivative is positive, which means that the critical point is a minimum.
Then, the dimensions for the package tht will minimize product cost are:
r = 3.43 cm