Optimization of surface area with a known perimeter.
You have 80 inches of wire. You can break it into two pieces or leave it intact. You're going to bend the pieces into squares. What are the maximum and minimum possible total areas of these squares?© SolutionLibrary Inc. solutionlibary.com 9836dcf9d7 https://solutionlibrary.com/math/linear-transformation/optimization-of-surface-area-with-a-known-perimeter-2kt
...o maximize(minimize) the total area, the problem boils down to:
>max(min) (x/4)^2 + ((80-x)/4)^2
Factor out and drop the constant 1/16, then take the derivative and set the equation equal to zero:
2x^2 - 160x + 6400 --> d/dx: 4x -160 = 0
Solving, we get x = ...