Multiple Choice
Identify the
choice that best completes the statement or answers the question.
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1.
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Find two positive numbers whose product is 181 and whose sum is a minimum.
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2.
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Find two positive numbers such that the sum of the first and twice the second is
56 and whose product is a maximum.
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3.
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Find the length and width of a rectangle that has perimeter 
meters and a maximum area. a. | 12 m; 12 m. | b. | 16 m; 9 m. | c. | 1m; 23
m. | d. | 13 m; 11 m. | e. | 6 m; 18 m. |
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4.
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Find the length and width of a rectangle that has an area of 968 square feet and
whose perimeter is a minimum.
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5.
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Find the point on the graph of the function  that is
closest to the point  . Round all numerical values in your answer to
four decimal places.
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6.
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A rectangular page is to contain  square inches of print. The
margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper
is used.
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7.
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Determine the dimensions of a rectangular solid (with a square base) with
maximum volume if its surface area is 529 square meters.
a. | Dimensions:  | b. | Dimensions:
 | c. | Dimensions:
 | d. | Dimensions:
 | e. | Dimensions:
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8.
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A Norman window is constructed by adjoining a semicircle to the top of an
ordinary rectangular window (see figure). Find the dimensions of a Norman window of maximum area if
the total perimeter is 38 feet. 
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9.
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A rectangle is bounded by the x- and y-axes and the graph of  (see figure). What length and width should the rectangle have so that its area is a
maximum?
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10.
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A solid is formed by adjoining two hemispheres to the ends of a right circular
cylinder. The total volume of the solid is 23 cubic centimeters. Find the radius, r, of the
cylinder that produces the minimum surface area. Round your answer to two decimal places.
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11.
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The sum of the perimeters of an equilateral triangle and a square is 19. Find
the dimensions of the triangle and the square that produce a minimum total area.
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12.
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A sector with central angle  is cut from a circle of
radius 10 inches, and the edges of the sector are brought together to form a cone. Find the magnitude
of  such that the volume of the cone is a
maximum.
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13.
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A farmer plans to fence a rectangular pasture adjacent to a river (see figure).
The pasture must contain 720,000 square meters in order to provide enough grass for the herd. No
fencing is needed along the river. What dimensions will require the least amount of
fencing?  a. | x = 600 and y = 1200 | b. | x = 1000 and y =
720 | c. | x = 1200 and y = 600 | d. | x = 720 and y =
1000 | e. | none of the above |
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