A page should have perimeter of 42 inches. The printing area within the page would be determined by top and bottom margins of 1 inch f

Question

A page should have perimeter of 42 inches. The printing area within the page
would be determined by top and bottom margins of 1 inch from each side, and the
left and right margins of 1.5 inches from each side. What should be the overall
dimensions of the page in order to maximize the printing area?

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Maria 2 weeks 2021-09-08T01:00:10+00:00 1 Answer 0

Answers ( )

    0
    2021-09-08T01:01:58+00:00

    Overall  dimensions of the page in order to maximize the printing area is  page should be 11 inches wide and 10 inches long .

    Step-by-step explanation:

    We have , A page should have perimeter of 42 inches. The printing area within the page  would be determined by top and bottom margins of 1 inch from each side, and the  left and right margins of 1.5 inches from each side. let’s assume  width of the page be x inches  and its length be y inches So,

    Perimeter = 42 inches

    2(x+y) = 42\\x+y = 21\\y = 21-x

    width of printed area = x-3  & length of printed area = y-2:

    area = length(width)

    area = (x-3)(y-2)\\area = (x-3)(21-x-2)\\area = (x-3)(19-x)\\area = -x^{2} + 22x -57

    Let’s find \frac{d(area)}{dx}:

    \frac{d(area)}{dx} = \frac{d(-x^{2}+22x-57)}{dx} = -2x +22 , for area to be maximum \frac{d(area)}{dx}= 0

    -2x+22 = 0\\2x =22\\x=11 inches

    And ,

    y = 21-x\\y = 21-11\\y = 10 inches

    Overall  dimensions of the page in order to maximize the printing area is  page should be 11 inches wide and 10 inches long .

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