if the printed area has width and height x and y, then the total area is
a = (x+8)(y+12)
and xy=384
a = (x+8)(384/x + 12) = 12x + 3072/x + 480
that is minimum when da/dx = 0, so we need
12 - 3072/x^2 = 0
x = 16
so the poster is (16+8) by (24+6) or 24x30
The top and bottom margins of a rectangular poster are 6 centimeters each, and the side margins are 4 centimeters each. If the area printed on the poster is fixed at 384 cm2,
a) Sketch the figure.
b) Find the dimensions of the poster using the least amount of paper.
1 answer
1 answer