and bottom and a 2-inch margin on each side. Find the overall dimensions that will minimize the total area
of the poster.
Answer: First, make a sketch.
Let the area of the picture be xy = 100. The total area of the poster is A = (x + 4)(y + 8). Then, expand the
equation.
A = xy + 4y + 8x + 32Substitute xy = 100 and y = into the area equation, and we get
A = 132 + + 8xNow take the derivative and set it equal to zero.
= 8 − = 0
Solving for x, we find that x = . Now solve for y by plugging x = into the area equation: y = 2
. Then check that these dimensions give us a minimum.