Answer:
Dimensions of the paper
height h = 9 in
length L = 6 in
A(min) = 54 in²
Step-by-step explanation:
Let x and y be dimensions of the print area then
x*y = 24 in² then y = 24/x
The total area is:
Heigth (h) h = y + 2*1.5 h = y + 3
lenght (L) L = x + 2
A(page) = h*L then
A = ( y + 3 ) * ( x + 2 )
A(x) = ( 24/x + 3 ) * ( x + 2 )
A(x) = 24 + 48/x + 3x + 6
A(x) = 30 + 48 /x + 3x
Taking derivatives on both sides of the equation
A´(x) = -48/x² + 3
A´(x) = 0 -48/x² + 3 = 0 -48/x² = -3
x² = 48/3 x² = 16 x = 4 in
and y = 24 / 4 = 6 in
Then dimensions of paper
h = y + 3
h = 9 in
L = x + 2
L = 4 + 2
L = 6 in
A(min) = 9*6
A (min) = 54 in²
