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

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 .