The top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm. the area of printed material on the poster is fixed at 1536 cm2. find the dimensions of the printed area that minimize the area of the whole poster.

Dimensions of printed poster are

length is 32 cm

width is 48 cm

Step-by-step explanation:

Let's assume

length of printed poster is x cm

width of printed poster is y cm

now, we can find area of printed poster

so, area of printed poster is

we are given that area as 1536

so, we can set it to 1536

now, we can solve for y

now, we are given

The top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm

so, total area of poster is

now, we can plug back y

now, we have to minimize A

so, we will find derivative

we can use product rule

now, we can simplify it

now, we can set it to 0

and then we can solve for x

Since, x is dimension

and dimension can never be negative

so, we will only consider positive value

now, we can solve for y

so, dimensions of printed poster are

length is 32 cm

width is 48 cm

if x = 1, then the answer is 3.5