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Operations Research and Optimization

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Consider the linear programming problem

Minimize
x_1+x_2

Subject to
2 x_1 + x_2 leq 0

x_1 - 2x_2 geq 0

x_1/3 - x_2 =10

You are to transform this problem to a form suitable for feeding to programs expecting the standard forms below. In each part, record the matrices f, A, and b suitable for feeding to a software package expecting each of the standard forms.

Part I.
Find what the arrays f_I, A_I, and b_I need to be to solve this problem using a software package that requires the standard form
min fx, ,,, Ax leq b,

Part II.
Find what the arrays f_{II}, A_{II}, and b_{II} need to be to solve this problem using a software package that requires the standard form
min fx, ,,, Ax leq b, x geq 0

Part III.
Find what the arrays f_{III}, A_{III}, and b_{III} need to be to solve this problem using a software package that requires the standard form
max fx, ,,, Ax = b, x geq 0.

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Solution Summary

The solution discusses operations research and optimization.

Solution provided by:
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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