A printer needs to make a poster that will have a total of 500 cm2 that will have 3 cm margins on the sides and 2 cm margins on the top and

Question

A printer needs to make a poster that will have a total of 500 cm2 that will have 3 cm margins on the sides and 2 cm margins on the top and bottom. What dimensions of the poser will give the largest printed area?

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Josie 2 weeks 2021-09-11T02:01:22+00:00 1 Answer 0

Answers ( )

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    2021-09-11T02:02:50+00:00

    Answer:

    The largest printed area is 381.43 cm^2 .

    Step-by-step explanation:

    The width of the full poster = 500/x

    Length of the printed area = l =x – 4

    Width of the printed area = w = (500/x) – 2

    Area of the printed space = (x – 4) × ((500/x) – 2)

    Now, take derivative of the area

    A’ = (x – 4)×(-500/x^2) + ((500/x) – 2)

    A’ = (2000/x^2) – 2

    A’ = (2000-2x^2) / x^2

    put derivative equal to zero like A’ = 0

    (2000-2x^2) / x^2 = 0

    2000 = 2x^2

    x^2 = 1000

    x = 31.62

    So, the length of the original poster is = x = 31.62 cm

    The width of the full poster = 500/x = 15.81 cm

    l = x – 4 = 27.62

    w = 500/x – 2 = 13.81

    Therefore, The area of space available for printing is = l × w

    = 27.62 × 13.81 = 381.43 cm^2 .

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