# The top and bottom margins of a poster are 4 cm and the side margins are each 6 cm. If the area of printed material on the poster is fixed at 384 square centimeters, how do you find the dimensions of the poster with the smallest area?

##### 1 Answer

#### Answer:

Draft

#### Explanation:

Let a be the width of the poster and b the height.

Let A be the area of the poster to be minimized.

(In this explanation I will omit all the "cm").

As the sum of the illustrated parts:

So let's get a in function of b:

Now,

I have to find the first derivative of the function to minimize it:

The minimum points satisfy the condition

But for obvious reason (b is the height of a poster), b must be positive, so only b=24 is a correct solution.

Now we have to find a:

So, the solution to the problem is