Question

A poster whose area is 180 square inches, has 1 inch margin at bottom and on sides 2 inch margin at the top. What are its dimensions for which printed area is maximized?

Answer 1

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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