Question

A printer needs to make a poster that will have a total of 125 cm2 that will have 0.5 cm margin on the bottom, 1 cm margin on the right, 2 cm margin on the left and 4 cm margin on the top. what dimensions of the poster will give the largest printed area?

Answer 1

To maximize the printed area within a poster of total area 125 cm2, one must minimize the margin area and adjust the dimensions accordingly, which involves calculus to optimize the dimensions for the largest printed area.

Step-by-step explanation:

The question asks us to find the dimensions of a poster that will have the largest printed area, given a total area of 125 cm2 and specific margin widths. To maximize the printed area, we must minimize the area taken by the margins. The combined width of the left and right margins is 2 cm (left) + 1 cm (right) = 3 cm, and the combined height of the top and bottom margins is 4 cm (top) + 0.5 cm (bottom) = 4.5 cm.

Let's denote the width of the printed area as w and the height as h. The total width of the poster is then w + 3 cm, and the total height is h + 4.5 cm. Given the total area (125 cm2), we can set up the equation: (w + 3)(​h + 4.5) = 125.

To maximize the printed area, we must optimize the dimensions w and h. This typically involves calculus, specifically finding the critical points of the function that represents the printed area and determining which gives the maximum area under the given constraints.