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Answer:
Therefore the dimension of the poster is 12 cm by 8 cm.
Step-by-step explanation:
Let the length of the poster be x and the width be y.
Given that the area of the poster is 96 cm².
∴xy =96
The sides margins each are 2 cm and the top and bottom margins of the poster are each 3 cm.
The length of printing space is =(x- 2.3) cm
= (x-6) cm
The width of the printing space is =(y-2.2) cm
=( y-4 )cm
The area of the printing space is A=(x-6)(y-4) cm²
∴A=(x-6)(y-4)
[ Putting
]
Differentiating with respect to x
Again differentiating with respect to x
To find the minimum area, we set A'=0
Dimension can't be negative.
Therefore x=12
If x=12, the value of A''>0,then at x=12, the area of the poster will be minimum.
If x=12, the value of A''<0,then at x=12, the area of the poster will be minimum.
Therefore at x= 12 cm the area of the poster will be maximum.
The width of the poster is = 8 cm
Therefore the dimension of the poster is 12 cm by 8 cm.