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Unformatted text preview: reserves direct at the General, Health, Law, Oxford, and Theology Libraries The United States copyright law (Title 17 of the US Code) governs the making of
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Y. x1 (leb Optimization Problems U§ A rectangular corral is to be constructed along a river. It is to be fenced on
3 sides with fencing which costs $10 per foot and is to have a divider down the (b) An aquarium is to be 6 ft. high and to have a volume of 750 cu ft. The base,
ends, and back are to be made of slate but the front is to be made of plate
glass, which costs 1.5 times as much as the slate per sq. ft. What dimen Front 10 x 6 ft
Sides 12.5 x 6 ft. (c) A square piece of cardboard with each side 12 in lOng has a square cut out at each corner. The sides are then turned up to form an open box, Find the side
of the cutout square that will produce a box of maximum yglume, (2 in) (J)A rectangular page is to contain 24 square inches of print. The
margins at the top and bottom of the page are each 1% inches.
The margins on each side are 1 inch. What should the dimensions of the page be so that the least amount of paper is used?
(6 in X 9 in) (f9 Two posts, one 12 feet high and the other 28 feet high, stand
30 feet apart. They are to be stayed by two wires, attached to
a single stake as follows:
stake 28 ft.
12 ft. 96 (3) A rancher has 200 feet of fencing to enclose two adjacent rectangular
corrals. What is the maximum area that can be enclosed? [A = 5000 ftz] 3 (h) An oil pipeline is to be built from a point A to a point B on the opposite
side of a 1/2 mile wide river and 5 miles upstream from A. If the pipe
under the river costs twice as much as the pipe used on dry land, how
should the pipe be laid so as to minimize the cost of the pipeline? 5 mi——————————§>B A (ans. so thatjDQ = _l mi) J1? (L) A couple wishes to fence 7200 ft2 rectangular plot for theirvdogs. One
side of the rectangle is to border a straight road, and the fence for that
side must be ornamented, costing three times as much per foot as the rest of the fence. Find the dimensions of the plot for the most economical
fencing. (60 ft X 120 ft) (éi) An opentopped rectangular box with reinforced square bottom and volume
96 ft is to be constructed. If the material for the bottom costs three times as much per square foot as material for the sides, find the dimensions
of the box that costs the least to make. [4 ft X 4 ft X 6 ft] P"? Arlswens
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