Answer:
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