Answer:
A(min) = 711,60 cm²
L = 15,40 cm
D = 46,21 cm
Step-by-step explanation:
Let L and D the lenght and height of the poster
and x and y dimensions of printed area so
L = y + 12 and D = x + 4
Printed area = 390 cm² and Pa = x*y then y = 390/x
Poster area is Ap = L * D = (y + 12 ) * ( x + 4 )
A(x) = ( 390/x + 12 ) * ( x + 4 )
A(x) = 390 + 1560/x + 12x + 48
A(x) = 438 + 1560/x + 12x
Taking derivatives on both sides of the equation
A´(x) = 12 - 1560/x²
A´(x) = 0 12 - 1560/x² = 0 12x² = 1560
x² = √ 130
x = 11.40 cm then y 390/ 11,40 y = 34,21 cm
And L = 11,40 + 4 L = 15,40 cm
And D = 34,21 + 12 D = 46,21 cm
A(min) = 15,40* 46,21
A(min) = 711,60 cm²
