Linear Programming by the Simplex Method and Input-Output Matrices ( Input/Output Matrix ) (13 Problems)
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Solution Summary
Thirteen problems relating to Linear Programming by the Simplex Method and Input-Output Matrices are investigated. The solution is detailed and well presented.
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Question (1) No correct answer.
As we can introduce new variables to write the inequalities to equalities as follows.
So, (A) could be correct if we changed the 4th 5th and 6th columns to be
-1 0 0
0 -1 0
0 0 -1
0 0 0
Question (2) (D)
The original LP and dual LP will have the equal optimal value 898.40. However, the solution corresponds to the coefficients in the dual objective function in the final tableau. Namely, x1=3.5, x2=4.0 and x3=2.4 in the 4th row.
Question (3) (B)
As we can introduce new variables to write the inequalities to equalities as follows.
Then we can see that only (B) has the first three rows match to the coefficients of the above equalities.
Question (4) (D)
Question (5) (A)
I attached the following tableaus.
Tableau #1
x y s1 s2 z
2 1 1 0 0 24
1 3 0 1 0 37
-10 -10 0 0 1 0
Tableau #2
x y s1 s2 z ...
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
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- "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."
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