Math 484.1 March 27, 2013. Midterm 2.
10 problems, 5 pts each. Write your name here ____________________________ and return the page even if you wrote nothing else on it.
26. The linear program x+y -> max, 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 equation ty = sin(t) has a solution for y.
(A) True. (B) False. (C) This is not a linear equation.
28. The linear program given by the standard row tableau
x y z 1
1 -1 0 0 = u
1 1 -1 5 -> min
(A) is infeasible, (B) is unbounded, (C) has an optimal solution, (D) the tableau is not standard
29. The following choice of the pivot entry in the following standard row tableau
x y z 1
1 -1* 0 0 = u
1 1 1 0 -> min
is (A) consistent with the simplex method, (B) inconsistent with the simplex method.
30. The following choice of the pivot entry in the standard row tableau
x y z 1
1 1* 0 -1 = u
-1 -2 1 0 -> min
is (A) consistent with the simplex method, (B) inconsistent with the simplex method.
31. For the linear program given by the standard row tableau
|
x |
y |
z |
1 |
|
|
1 |
-1 |
0 |
-1 |
= u |
|
1 |
-2 |
1 |
0 |
-> min |
x=0, y = 0, z = 0, u = -1 is (A) a feasible solution, (B) an optimal solution,(C) the basic solution.
32. The optimal value of the program x3+ty -> min, x2 ≤ 1, y2 ≤ 4
as a function of the parameter t has the following slopes: (A) 2, (B) 1,(C) 1,0, (D) 2, -2.
33. The optimal value of the program x+y -> min, |x| ≤ 3t+1, |y| ≤ 2t
as a function of the parameter t has the following slopes: (A) -3, (B) -5,(C) -3, 3.
34. The optimal value of the job assignment problem
|
3 |
0 |
3 |
1 |
2 |
1 |
|
3 |
1 |
3 |
2 |
2 |
1 |
|
3 |
3 |
5 |
2 |
4 |
2 |
|
3 |
2 |
4 |
2 |
2 |
2 |
|
1 |
1 |
3 |
1 |
3 |
1 |
|
2 |
2 |
2 |
1 |
1 |
0 |
is (A) < 8, (B) 8, (C) > 8.
35. The optimal value for the transportation problem
|
3 |
2 |
3 |
2 |
1 |
0 |
2 |
2 |
2 |
9 |
|
3 |
3 |
3 |
5 |
1 |
1 |
3 |
3 |
2 |
8 |
|
2 |
3 |
1 |
3 |
1 |
1 |
3 |
1 |
2 |
9 |
|
2 |
3 |
5 |
1 |
2 |
1 |
2 |
1 |
2 |
8 |
|
6 |
1 |
6 |
1 |
6 |
1 |
6 |
1 |
6 |
demand\supply |
is (A) ≤52, (B) >52.