Math 484.1 Nov 7, 2013. Midterm 2.
15 problems, 5 pts each. Write your name here Vaserstein and return the page even if you wrote nothing else on it.
26. The linear program x+y -> min, x ≥ 0, y ≤ 3
(A) is infeasible, (B) is unbounded, (C) has an optimal solution, (D) is not a linear program.
27. For every t, the linear equation tz = sin(z) has a solution for z.
(A) True. (B) False. (C) This is not a linear equation for z.
28. The linear program is given by the standard row tableau
x1 x2 x3 x4 x5 1
1 -1 0 0 7 0 = u
2 -2 0 0 -6 4 = v
3 -3 -5 6 5 0 -> min.
Here are all choices for the pivot entry that are consistent with the simplex method: (A) -1, (B) -6, (C) 3, (D) -1, -6, (E) none of the above.
29. The linear program is given by the standard row tableau
x1 x2 x3 x4 x5 1
1 -1 0 0 7 0 = u
2 -2 0 0 -6 -4 = v
3 1 -1 6 5 0 -> min.
Here are all choices for the pivot entry that are consistent with the simplex method: (A) 1, (B) 2, (C) 3, (D) 1, 2, (E) none of the above.
30. The linear program is given by the standard row tableau
x1 x2 x3 x4 x5 1
1 -1 0 0 7 0 = u
2 -2 0 0 -6 0 = v
3 1 1 6 5 -5 -> min.
Here are all choices for the pivot entry that are consistent with the simplex method: (A) 1 in x1 column, (B) 2, (C) -1, (D) 7, (E) none of the above.
The tableau is optimal.
31. For the linear program given by the standard row tableau
|
x |
y |
z |
1 |
|
|
1 |
-1 |
0 |
-2 |
= u |
|
1 |
-2 |
1 |
0 |
-> min |
x=0, y = 0, z = 0, u = -1 is (A) the basic solution, (B) an optimal solution, (C) none of the above.
32. The linear program given by the standard row tableau
|
x |
y |
z |
1 |
|
|
1 |
-1 |
0 |
-2 |
= u |
|
2 |
-2 |
1 |
0 |
-> min |
(A) is infeasible, (B) has an optimal solution, (C) is unbounded, (D) none of the above.
33. The optimal value of the program (sin x)2+t(cos y)2-> min, x2≤ 1, y2 ≤4
as a function of the parameter t has the following slopes: (A) 2, (B) -2,(C) 2, -2, (D) -1, 0.
None of the above answers is correct (5 pts for this).
The minimum is t when t ≤ 0 and 0 when t ≥ 0. So the slopes are 1 and 0 (two bonus points to be included into b2 at Angel for this).
34. The optimal value of the program x+y -> max, |x| ≤ 3t+1, |y| ≤ 2t
as a function of the parameter t has the following slopes: (A) -3, (B) 5, (C) -3, 3. (D) none of the above
35. The optimal value of the job assignment problem
|
3 |
0 |
3 |
1 |
2 |
1 |
|
3 |
1 |
3 |
1 |
2 |
1 |
|
3 |
3 |
5 |
2 |
4 |
1 |
|
3 |
2 |
4 |
2 |
1 |
2 |
|
1 |
1 |
3 |
1 |
3 |
1 |
|
2 |
2 |
2 |
1 |
1 |
1 |
is (A) 5, (B) 5.5, (C) 6, (D) none of the above.
36. The optimal value for the transportation problem
|
2 |
3 |
3 |
2 |
1 |
2 |
3 |
4 |
1 |
6 |
|
1 |
2 |
2 |
1 |
1 |
2 |
3 |
3 |
1 |
9 |
|
2 |
2 |
1 |
3 |
1 |
3 |
3 |
4 |
0 |
7 |
|
3 |
3 |
1 |
1 |
2 |
3 |
2 |
3 |
2 |
12 |
|
6 |
1 |
6 |
1 |
6 |
1 |
6 |
1 |
6 |
demand\supply |
is (A) 30, (B) 35, (C) 37, (D) none of the above.
37, There is a linear program with the feasible region given by x2 ≤ 1, y2 ≤ 4 and exactly one optimal solution
x= 1, y = 2. (A) True. (B) False.
38. For any feasible tableau with 2 columns, the simplex method terminates in at most one pivot step.
(A) True. (B) False
39. x > 2 only if x ≥ 0.
(A) True. (B) False.
40. x > 2 provided that x ≥ 0.
(A) True. (B) False.