# Section 3.6 Optimization Problems

Education

15

All Questions

15

Multiple Choice

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True False

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Essay

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Short Answer

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Not Answered

Q 1

Find two positive numbers whose product is 186 and whose sum is a minimum.
A)
B)
C)
D)
E)

Free

Multiple Choice

A

Q 2

Find two positive numbers such that the sum of the first and twice the second is 96 and whose product is a maximum.
A)48 and 48
B)48 and 24
C)42 and 27
D)54 and 21
E)44 and 26

Free

Multiple Choice

B

Q 3

Find the length and width of a rectangle that has perimeter 40 meters and a maximum area.
A)10 m;10 m.
B)14 m;7 m.
C)1 m;19 m.
D)11 m;9 m.
E)5 m;15 m.

Free

Multiple Choice

A

Q 4

Find the length and width of a rectangle that has an area of 1,152 square feet and whose perimeter is a minimum.
A) feet; feet
B) feet; feet
C) feet
D) feet; feet
E) feet; feet

Multiple Choice

Q 5

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.
A)
B)
C)
D)
E)

Multiple Choice

Q 6

Find the point on the graph of the function that is closest to the point .
A)
B)
C)
D)
E)

Multiple Choice

Q 7

A rectangular page is to contain 196 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.
A)17,17
B)29,29
C)18,18
D)15,15
E)16,16

Multiple Choice

Q 8

On a given day,the flow rate F (cars per hour)on a congested roadway is given by ,where v is the speed of the traffic in miles per hour.What speed will maximize the flow rate on the road? Round your answer to the nearest mile per hour.
A)19 miles per hour
B)17 miles per hour
C)18 miles per hour
D)10 miles per hour
E)20 miles per hour

Multiple Choice

Q 9

Determine the dimensions of a rectangular solid (with a square base)with maximum volume if its surface area is 121 square meters.
A)Dimensions:
B)Dimensions:
C)Dimensions:
D)Dimensions:
E)Dimensions:

Multiple Choice

Q 10

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.
A) feet; feet
B) feet; feet
C) feet; feet
D) feet; feet
E) feet; feet

Multiple Choice

Q 11

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?
A)
B)
C)
D)
E)

Multiple Choice

Q 12

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder.The total volume of the solid is 28 cubic centimeters.Find the radius,r,of the cylinder that produces the minimum surface area.Round your answer to two decimal places.
A) cm
B) cm
C) cm
D) cm
E) cm

Multiple Choice

Q 13

The sum of the perimeters of an equilateral triangle and a square is 8.Find the dimensions of the triangle and the square that produce a minimum total area.
A)side of square: ;side of triangle:
B)side of square: ;side of triangle:
C)side of square: ;side of triangle:
D)side of square: ;side of triangle:
E)side of square: ;side of triangle:

Multiple Choice

Q 14

A sector with central angle is cut from a circle of radius 4 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.
A) radians
B) radians
C) radians
D) radians
E) radians

Multiple Choice

Q 15

Assume that the amount of money deposited in a bank is proportional to the square of the interest rate the bank pays on this money.Furthermore,the bank can reinvest this money at .Find the interest rate the bank should pay to maximize profit.(Use the simple interest formula. )
A)
B)
C)
D)
E)

Multiple Choice