course Mth 272 §ñÜZ€ŠÇ…†¦ê›ƒ ²L¼F¸¼œ°žjÒY¦È†ò¬•êassignment #027 027. Applied Calculus II 07-29-2008
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15:52:47 Query problem 7.3.38 level curves of e^(xy) for c = 1, 2, 3, 4, 1/2, 1/3, 1 / 4
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RESPONSE --> I think this is the same first problem as in assignment # 26. The contour curves appear to be very steep around the x axis and then level out as they move away from the x axis. confidence assessment: 2
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15:58:07 What is the level curve for c = 1? Describe the curve and give the value of e^(xy) at any point on the curve.
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RESPONSE --> well, my understanding of c is that it's the plane for the intersection of the surface at z = e^xy. i'm not sure how to describle it. at point (2,2) the value would be e^(xy) e^(4) = 54.598 do we use the Cobb-Douglas theorem here? confidence assessment: 0
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16:01:27 Give the level curves for the other indicated values of c.
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RESPONSE --> well, we aren't given any numbers to plug in for teh cobb-douglas production function, so I guess we do not use that. looking at the calculator you have from c = 1 to c = 2, the level curve is not very steep, from c= 2 to c = 3, the level curve is not very steep at all, from c = 3 to c = 4, the level curve is not steep, from c = 4 to c =1/2, the level curve is steep and is right next to curve of c = 1 from c = 1/2 to c = 1/3, the level curve is even steeper from c = 1/3 to c =1/4, the level curve is even steeper than previous. confidence assessment: 1
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16:04:27 Describe the 'topographic map' you would get from these level curves.
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RESPONSE --> depending on what the toographic map was measuring... if it was measuring a ""mountain and valley"" surface then you would have the flat valley from c =1 to c =4 and then from c =4 to c =1/4 you would have the mountain with the steepness of it increasing as you get closer to c = 1/4. confidence assessment: 1
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16:06:25 If you walked along this 'map' at an angle or 45 degrees to the positive x axis, how would your indicated elevation change? Would your path indicate a hill of increasing, constant, or decreasing steepness, and how can you tell?
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RESPONSE --> increasing steepness, because the c = 1/4 level is closer to the x axis and that is what you are approaching. confidence assessment: 2
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16:07:36 Query problem 7.3.46 queuing model W(x,y)=1/(x-y), x=ave service rate, y ave arrival rate
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RESPONSE --> at (15, 10) W(15,10) = 1 / (15-10) = .2 at (12,9) W (12, 9) = 1 / (12-9) = .33 at (12, 6) W (12, 6) = 1 / (12-6) = .50 at (4, 2) W (4,2) = 1 / (4-2) = .50 confidence assessment: 2
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16:07:48 What are the specified points and what is the value of W at each point?
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RESPONSE --> previously answered confidence assessment:
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16:09:21 Why is the function defined only for y < x?
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RESPONSE --> because if y was greater than x then you would have a (1 / - number ) which would give you not give you a sensible amoutn of time that a customer waits in line. confidence assessment: 1
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16:10:44 Your instructor thinks that maybe the text got the definitions of x and y reversed. Why might this be inferred from the meaning of the model (e.g., would we expect W to be positive or negative if the service rate exceeds the arrival rate)?
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RESPONSE --> oh, well yeah I guess one would suspect right off the tops of their head to expect W to be negative if the service rate exceeds the arrival rate, because that would be a bad or ""negative"" thing for the customer confidence assessment: 2
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