Optimization (Calculus)
48 videos • 18,680 views • by WNY Tutor
1
A closed cylindrical tank with a flat bottom and an inverted hemispherical top is to have a volume o
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2
A woman at a point A on the shore of a circular lake with radius 2 mi wants to arrive at the point C
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3
Find an equation of the line through the point (3,5) that cuts off the least area from the first qua
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4
A cylindrical can without a top is made to contain V cm3 of liquid. Find the dimensions that will mi
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5
A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the win
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6
Find the area of the largest rectangle that can be inscribed in a right triangle with legs of length
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7
A fence 8 ft tall runs parallel to a tall building at a distance of 4 ft from the building. What is
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8
The top and bottom margins of a poster are each 3 cm and the side margins are each 2 cm. If the area
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9
An oil refinery is located on the north bank of a straight river that is 2 km wide. A pipeline is to
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10
Textbook Answers - Stewart Calculus
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11
A box with a square base and open top must have a volume of 32,000 cm3.
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12
Find two numbers whose difference is 100 and whose product is a minimum.
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13
The sum of two positive numbers is 16. What is the smallest possible value of the sum of their squar
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14
What is the minimum vertical distance between the parabolas y = x^2 + 1 and y = x - x^2?
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15
The rate at which photosynthesis takes place for a species of phytoplankton is modeled by the functi
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16
The manager of a 100-unit apartment complex knows from
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17
A rectangular storage container with an open top is to have a volume of 10 m3. The length of its bas
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18
A steel pipe is being carried down a hallway 9 ft wide. At the end of the hall there is a right-angl
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19
A boat leaves a dock at 2:00 PM and travels due south at a speed of 20 km/h. Another boat has been h
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20
Sandy is making a closed rectangular jewelry box with a square base from two different woods
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21
A corridor that is 3 m wide makes a right-angle turn, as shown on the left
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22
A farmer wants to fence an area of 1.5 million
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23
A poster is to have an area of 180
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24
A kite 100 ft above the ground
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25
If 1200 cm2 of material is available
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26
Find the point on the curve y=sqrt(x) that is closest to (3 0)
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27
Of all numbers whose sum is 50 find the two that have the maximum product
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28
Each unit of a product can be made on either machine a or machine b
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29
What is the shortest possible length of the line segment that is cut off
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30
Where should the point p be chosen
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31
A cone shaped drinking cup is made from a circular
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32
Find the area of the largest trapezoid that can be inscribed in a circle
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33
A rain gutter is to be constructed from a metal sheet
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34
During the summer months terry makes and sells
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35
A piece of wire 10 m long is cut
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36
The illumination of an object by a light source
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37
Find the dimensions of the rectangle with area
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38
What is the maximum vertical distance between the line
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39
An observer stands at point p one unit away from a track
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40
A painting in an art gallery has height
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41
If you are offered one slice from a round pizza
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42
A rectangle has its base on the x axis
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43
A farmer has 1200 feet of fencing for enclosing a trapezoidal field
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44
A box with an open top is to be constructed from a 4ft by 3ft
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45
If the two equal sides of an isosceles triangle have length a
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46
A model used for the yield y
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47
A rectangular plot of farmland will be bounded
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48
A baseball team plays in a stadium that holds
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