15 items are filed under this topic.
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The maximum area of a garden |
2021-04-28 |
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From Lexie:
suppose you want to make a rectangular garden with the perimeter of 24 meters.
What's the greatest the area could be and what are the dimensions?
Answered by Penny Nom. |
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The maximum volume of a cone |
2019-07-14 |
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From A student:
find the maximum volume of a cone if the sum of it height and volume is 10 cm.
Answered by Penny Nom. |
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A Max/Min problem with an unknown constant |
2016-01-17 |
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From Guido:
Question:
The deflection D of a particular beam of length L is
D = 2x^4 - 5Lx^3 + 3L^2x^2
where x is the distance from one end of the beam. Find the value of x that yields the maximum deflection.
Answered by Penny Nom. |
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A calculus optimization problem |
2015-05-14 |
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From Ali:
Given an elliptical piece of cardboard defined by (x^2)/4 + (y^2)/4 = 1. How much of the cardboard is wasted after the largest rectangle (that can be inscribed inside the ellipse) is cut out?
Answered by Robert Dawson. |
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Largest cone in a sphere |
2015-01-15 |
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From Alfredo:
What is the altitude of the largest circular cone that may be cut out from a sphere of radius 6 cm?
Answered by Penny Nom. |
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Maximize profit |
2013-01-19 |
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From Chris:
A firm has the following total revenue and total cost function.
TR=100x-2x^2
TC=1/3x^3-5x^2+30x
Where x=output
Find the output level to minimize profit and the level of profit achieved at this output.
Answered by Penny Nom. |
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A maximization problem |
2012-04-09 |
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From Nancy:
After an injection, the concentration of drug in a muscle varies according to a function of time, f(t). Suppose that t is measured in hours and f(t)=e^-0.02t - e^-0.42t. Determine the time when the maximum concentration of drug occurs.
Answered by Penny Nom. |
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An optimization problem |
2010-05-23 |
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From Marina:
Hello, I have an optimization homework assignment and this question has me stumped..I don't even know A hiker finds herself in a forest 2 km from a long straight road. She wants to walk to her cabin 10 km away and also 2 km from the road. She can walk 8km/hr on the road but only 3km/hr in the forest. She decides to walk thru the forest to the road, along the road, and again thru the forest to her cabin. What angle theta would minimize the total time required for her to reach her cabin?
I'll do my best to copy the diagram here:
10km
Hiker_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _Cabin
\ | /
\ | /
f \ 2km /
\ | /
theta \___________________________ /
Road
Answered by Penny Nom. |
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A max min problem |
2010-04-06 |
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From Terry:
The vertex of a right circular cone and the circular edge of its base lie on the surface of a sphere with a radius of 2m. Find the dimensions of the cone of maximum volume that can be inscribed in the sphere.
Answered by Harley Weston. |
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Maximize revenue |
2008-10-08 |
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From Donna:
A university is trying to determine what price to charge for football tickets. At a price of 6.oo/ticket it averages 70000 people per game. For every 1.oo increase in price, it loses 10000 people from the average attendance. Each person on average spends 1.5o on concessions. What ticket price should be charged in order to maximize revenue.
price = 6+x, x is the number of increases.
ticket sales = 70000- 10000x
concession revenue 1.5(70000 - 10000x)
I just do not know what to do with the concession part of this equation
(6+x) x (70000 - 10000x) I can understand but not the concession part please help. thx.
Answered by Penny Nom. |
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Optimization - carrying a pipe |
2007-05-05 |
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From A student:
A steel pipe is taken to a 9ft wide corridor. At the end of the corridor there is a 90° turn, to a 6ft wide corridor. How long is the longest pipe than can be turned in this corner?
Answered by Stephen La Rocque. |
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A cylinder inside a sphere |
2007-04-25 |
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From Louise:
i need to find the maximum volume of a cylinder that can fit inside a sphere of diamter 16cm
Answered by Penny Nom. |
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A Norman window |
2006-11-30 |
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From Joe:
a norman window is a rectangle with a semicircle on top. If a norman window has a perimeter of 28, what must the dimensions be to find the maximum possible area the window can have?
Answered by Stephen La Rocque. |
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How much labor should the firm employ? |
2006-10-28 |
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From Christy:
A dressmaking firm has a production function of Q=L-L(squared)/800. Q is the number of dresses per week and L is the number of labor hours per week. Additional cost of hiring an extra hour of labor is $20. The fixed selling price is P=$40. How much labor should the firm employ? What is the resulting output and profit? I am having a difficult time with this, HELP!
Answered by Stephen La Rocque. |
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The box of maximum volume |
2006-02-01 |
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From Elizabeth:
A box factory has a large stack of unused rectangular cardboard sheets with the dimensions of 26 cm length and 20 cm width.
The question was to figure what size squares to remove from each corner to create the box with the largest volume.
I began by using a piece of graph paper and taking squares out. I knew that the formula L X W X H would give me volume. After trial and error of trying different sizes I found that a 4cm X 4cm square was the largest amount you can take out to get the largest volume. My question for you is two parts
First: Why does L X H X W work? And second, is their a formula that one could use, knowing the length and width of a piece of any material to find out what the largest possible volume it can hold is without just trying a bunch of different numbers until you get it. If there is, can you explain how and why it works.
Answered by Penny Nom. |
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