MATH 221 Class Exercises on Optimization
1. Find the maximum area of a rectangle whose base is on the x-axis and whose other two vertices are on the graph of y = 8 – x^2.
2. A farmer wishes to build a pasture as pictured below. What is the minimum length of fence he needs if the total area of the fenced in region is 30,000 square feet?
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3. Find the point (x,y) in the first quadrant on the line 4x+3y-12 = 0 such that the rectangle two of whose sides are on the x and y axes and whose other vertex is at (x,y) has maximum area.