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Problem Set #6 Curve Sketching, Applied Optimization Analyze and sketch the graph of the fol- 6. The United States Postal Service charges lowing functions. more for boxes whose combined length and girth exceeds " (the "length" of a package is the length of its longest side; 1. f(x) = x - 2 3 the girth is the perimeter of the cross secon, i.e., 2w + 2h). What is the maxi- mum volume of a package with a square cross section (w = h) that does not ex- 3x 2. f(x) = - ceed the " standard? 12 - 1 7. A farmer plans to fence a rectangular 3. f(x) = 3x4+ 423 pasture adjacent to a river. The pasture must contain 245,000 square meters to provide enough grass for the herd. What 4. f(x) = XV4 - 12 dimensions will require the least amount of fencing if no fencing is needed along the river? 5. A standard soda can is roughly cylindri cal and holds cm of liquid. What di- mensions should the cylinder be to min- 8. A manufacturer wants to design an open imize the material needed to produce the box with a square base and a surface area can? Based on your dimensions, deter- of 108 square inches. What dimensions mine whether or not the standard can is will produce a box with, maximum vol- produced to minimize the material costs. umc