Feedback — Linear Programming
You submitted this quiz on Wed 1 May 2013 1:51 PM PDT -0700. You got a score of 2.80 out of 3.00. You can attempt again, if you’d like.
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Question 1
(seed = 735654) Which of the following constraints can be modeled using linear programming?
| Your Answer | Score | Explanation | |
|---|---|---|---|
x1 - 2x2 - 3x3 - 4x4 <= 10. |
✔ | 0.20 | |
x1 - 2x2 - 3x3 - 4x4 <= -10. |
✔ | 0.20 | |
x1, x2, x3, x4 are either 0 or 1 |
✔ | 0.20 | |
x1, x2, x3, x4 are unconstrained |
✘ | 0.00 | |
x1 + 1/2 x2 + 1/3 x3 + 1/4 x4 <= 10. |
✔ | 0.20 | |
| Total | 0.80 / 1.00 |
Question Explanation
Question 2
(seed = 42623)
Consider the following linear programming simplex tableaux with 3 equations and 8 variables:
maximize Z
- 10/3 x0 + 2 x1 + 1 x2 + 1/4 x6 - 3/5 x7 - Z = -210
---------------------------------------------------------------------------------------------------------
- 1 x0 - 5/2 x1 - 10/3 x2 + 1 x4 + 7/5 x6 + 9/5 x7 = 6
+ 9/2 x0 - 10 x1 - 4/3 x2 + 1 x5 + 8 x6 + 4 x7 = 54
- 1 x0 + 1 x1 - 1 x2 + 1 x3 - 10 x6 + 3 x7 = 54
x0 , x1 , x2 , x3 , x4 , x5 , x6 , x7 >= 0
Which variable could be the next to *enter* the basis? Check all that apply.
| Your Answer | Score | Explanation | |
|---|---|---|---|
x0 |
✔ | 0.12 | |
x1 |
✔ | 0.12 | |
x2 |
✔ | 0.12 | |
x3 |
✔ | 0.12 | |
x4 |
✔ | 0.12 | |
x5 |
✔ | 0.12 | |
x6 |
✔ | 0.12 | |
x7 |
✔ | 0.12 | |
| Total | 1.00 / 1.00 |
Question Explanation
The basis is { x4, x5, x3 }.
The nonbasic variables are { x0, x1, x2, x6, x7 }.
The entering variables are those nonbasic variables with a positive objective function coefficient.
Question 3
(seed = 522611)
Consider the following linear programming simplex tableaux with 5 equations and 9 variables:
maximize Z
- 3/4 x2 + 9/5 x3 - 9/5 x5 - 3/2 x7 - Z = -246
--------------------------------------------------------------------------------------------------------------------
- 7/5 x2 - 1/4 x3 - 3 x5 + 2 x7 + 1 x8 = 42
+ 1/5 x2 + 2 x3 + 1 x4 - 9/5 x5 - 2/5 x7 = 18
+ 1 x0 - 1/3 x2 + 9/4 x3 + 2/5 x5 + 10 x7 = 6
+ 1 x1 - 1 x2 - 4/5 x3 - 7/3 x5 + 6 x7 = 30
+ 5 x2 + 4 x3 + 7/2 x5 + 1 x6 - 5/2 x7 = 30
x0 , x1 , x2 , x3 , x4 , x5 , x6 , x7 , x8 >= 0
Suppose that variable x3 is the variable chosen to enter the basis.
Which variable could be the next to *leave* the basis? Check all that apply.
| Your Answer | Score | Explanation | |
|---|---|---|---|
x0 |
✔ | 0.11 | |
x1 |
✔ | 0.11 | |
x2 |
✔ | 0.11 | |
x3 |
✔ | 0.11 | |
x4 |
✔ | 0.11 | |
x5 |
✔ | 0.11 | |
x6 |
✔ | 0.11 | |
x7 |
✔ | 0.11 | |
x8 |
✔ | 0.11 | |
| Total | 1.00 / 1.00 |
Question Explanation
The basis is { x8, x4, x0, x1, x6 }.
The nonbasic variables are { x2, x3, x5, x7 }.
The entering variable is x3.
The min ratio test determines the leaving variable: min ratio = { *, 9, 8/3, *, 15/2 } = 8/3.
The minimum occurs in row 2, which corresponds to basic variable x0.
The leaving variables is x0.
