The dimensions for which the printed area is maximized are 16.432 × 10.954 in².
let the height of the poster = x inches
area of the poster = 180 in²
thus, its width is 180/x inches.
The printed area has a height of x - 3 inches due to the 1-inch bottom margin and 2-inch top margin.
The sides have a margin of 1 inch, so the width of the printed area is:
180/x - 2
the area of printed area A is given by the formula of a rectangle,
A = height × width
A = (x-3)(180/x - 2)
A = 180 - 2x - 540/x + 6
the maximized area is when dA/dx = 0
dA/dx = - 2 - 540(- 1/x²) = 0
540/x² = 2
x = √270
hence height = √270 = 16.432 inches,
and width = 180/√270 = 10.954 inches.
know more about the maximized area here: brainly.com/question/28821169
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