Your challenge is to create a cylindrical can that minimizes the cost of materials but must hold 100 cubic inches. The top and bottom of the can cost $0.014 per square inch, while the sides cost only $0.007 per square inch. Show how you did it too?

and

Step-by-step explanation:

Given

-- Top and Bottom

--- Sides

Required

What dimension of the cylinder minimizes the cost

The volume (V) of a cylinder is:

Substitute 100 for V

Make h the subject

The surface area (A) of a cylinder is:

Where

So, the cost of the surface area is:

Substitute

Open bracket

To minimize, we differentiate C w.r.t r and set the result to 0

Set to 0

Collect Like Terms

Cross Multiply

Make the subject

Take cube roots of both sides

Recall that:

Hence, the dimensions that minimizes the cost are:

and

To calculate the cost, we have:

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