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 poster will give the largest printed area?

Answer 1

width of 27.386 cm and height of 18.257

Explanation:

Let x = width of entire poster.

Area of entire poster is 500 cm².

Height of entire poster is area/width = 500/x

area of printed are = (x - 6)(500/x - 4)

A = 500 - 4x - 3000/x + 24

A = -4x - 3000/x + 524

Now we take the derivative of the area with respect to the width, x.

A' = -4 + 3000/x²

A' = 3000/x² - 4

Set the derivative equal to zero and solve for x to find a maximum value.

3000/x² - 4 = 0

3000/x² = 4

4x² = 3000

x² = 750

x = 27.386

500/27.386 = 18.257

Answer: width of 27.386 cm and height of 18.257