Expert: Paul Klarreich - 4/28/2009

Question
1. Find the dimensions of the largest rectangle whose perimeter is 3200 feet. (Enter the dimensions from smallest to largest.)
Side:
Side:
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2. A farmer wishes to build a large rectangular grazing area of dimensions, width, w, and length, l,splitting the area in to 4 equal fields by dividing the width into 4 equal pieces. The total area of all the fields must be 10000 square feet. Find the dimensions that uses the least amount of fencing.
(It is not always the case that the width is shorter than the length. Round-off your answers to 3 decimal places.)

Width w =
Length l =
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3. A large bin for holding heavy material must be in the shape of a box with an open top and a square base. The base will cost 6 dollars a square foot and the sides will cost 8 dollars a foot. If the volume must be 110 cubic feet. Find the dimensions that will minimize the cost of the box's construction.

Base :
Each side :
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4. A 30 by 30 square piece of cardboard is to be made into a box by cutting out equal square corners from each side of the square. What size corners should be cut out so that the volume of the box is maximized?

Length of each corner :
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5. A rectangular page is to contain 155 square inches of print. The top and bottom margins are each 0.8 inches wide , and the margins on each side is 1.5 inches wide. What should the dimensions be if the least amount of material is to be used ?

Length of top(bottom) : __ inches
Length of side : ___ inches
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6. Suppose postal requirements are that the maximum of the length plus the girth (cross sectional perimeter) of a rectangular package that may be sent is 225 inches. Find the dimensions of the package with square ends whose volume is to be maximum.

Square side :
Length :
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7.
Bob is at point B 30 miles from A. Alice is in a boat in the sea at point C 1.5 miles from the beach. Alice rows at 2 miles per hour and walks at 4.25 miles per hour , where along the beach should she land so that she may get to Bob in the least amount of time ?

Distance of landing point measured from A : ___ miles.  

Answer
Hi, Lily,

Some other expert sent this to the question pool.  I am sure it is because you just dumped your homework on us, and this is not a 'do-your-homework-for-you site.

But you can still get answers to these.

Click 'Browse Past Answers'
Look for MAXIMUM-MINIMUM PROBLEM as the subject line.

Good hunting.