Answer:
The smallest poster has dimension 25.6 cm by 32.05 cm.
Step-by-step explanation:
Let "x" and "y" be the length and the width of the poster.
The margin of a poster are 4 cm and the side margins are 5 cm.
The length of the print = x - 2(4) = x - 8
The width of the print = y - 2(5) = y - 10
The area of the print = (x- 8)(y -10)
The area of the print is given as 388 square inches.
(x-8)(y -10) = 388
From this let's find y.
y -10 =
y = -------------------(1)
The area of the poster = xy
Now replace y by , we get
The area of the poster = x ()
=
To minimizing the area of the poster, take the derivative.
A'(x) =
A'(x) =
Now set the derivative equal to zero and find the critical point.
A'(x) = 0
= 0
Taking square root on both sides, we get
x - 8 = 17.6
x = 17.6 + 8
x = 25.6
So, x = 25.6 cm takes the minimum.
Now let's find y.
Plug in x = 25.6 cm in equation (1)
y =
y = 22.05 + 10
y = 32.05
Therefore, the smallest poster has dimension 25.6 cm by 32.05 cm.