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Minimization and contour point

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Consider the minimization of *see attached for equation*
subject to the constraint of *see attached for equation*

(a) Graph the contour point of with y-axis
and x-axis between -2 and 6.(on my paper there is a dot (between point (3,3)
Estimate where extrema values may occur and compute the function values
corresponding to these extrema.

(b) Solve the problem in part (a) with the aid Lagrange multipliers. You may
have to solve the equations numerically. Compare your answers with those in
the part (a).

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Solution Summary

This set looks at minimization, contour points, and Lagrange multipliers.

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See attachment please!

Consider the minimization of
subject to the constraint of

(a) Graph the contour point of with y-axis
and x-axis between -2 and 6.(on my paper there is a dot (between point (3,3)
Estimate where extrema values may occur and compute the function values
corresponding to these extrema.

Solution. We used Maple and got the following graph

where the green curves represent the contour lines of f(x,y) and from left to right, its value increases. The red one is the circle defined by

Since we need to find the minimization of f(x,y) under a constraint . So, by the above graph, we can estimate the ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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