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1. A farmer needs to enclose a rectangular pasture containing 1,600,000 square feet. Along
the road adjoining his property, he wants to use an expensive fence that costs $15 per
foot. A river runs perpendicular to the road; he will need no fence on that side. The
cheaper fence for the remaining two sides costs $10 per foot. What dimensions will
minimize the cost of fencing the pasture?
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3. Postal restrictions limit the size of packages that can be sent through the mail. Suppose
the length of the package plus the distance around it (its girth) may not exceed 108
inches. Find the volume of the largest box with square cross section that can be mailed.
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4. A rectangular
12-inch sides.
folded into an
the volume of
box with a square base is to be formed from a square piece of metal with
A square piece will be cut from each corner of the sheet, and it will be
open box. What size square should be cut from each corner to maximize
the box?
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