Midterm 1 Feb 19, 2016.  Math 484.002 25 questions, 2 pts each.

Name  Dr.V

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Answers are in boldface Details are not given.

1. 0 < 0   is

(A) a linear constraint for x, (B) an affine function of x  (C) a linear form in x, (D) an equation.

E.

2.   x    - 1  is

(A) a linear constraint for x, y,  (B) a linear equation for x, y  in standard form,

(C) an affine function of x, y,  (D) an equation  with no solutions,

C.

3. Every linear program  with no constraints than the number of unknowns

(A) is unbounded,  (B) is infeasible,  (C)  has many optimal solutions, (D) is feasible.

E.

4. For any given numbers a, b, the mathematical  program   a2x + b  -> min, 0 ≤  x    1  with an unknown  x

(A)  it is not a linear program , (B)   is unbounded, (C) has  many  optimal solutions   (D) is  feasible.

D.

5. The mathematical program y/x -> min subject to |x| <  1, y > 0 for two unknowns x, y

(A) is a linear program, (B) is infeasible, (C) has an optimal solution,(D) is unbounded.

D.

6. The minimal total time for the job assignment problem

6  2  1  4

3  0  2  1

2  5  3  6

1  1  2  3

is    (A) 4,  (B) 5,  (C) 6, (D) 7.

B.

7. For each  number  t, the equation     (cos(t) -2)x= sin(t)  for unknown x

(A) is not linear, (B) has exactly one  solution, (C) is unbounded, (D) has many solutions.

B.

8, If x≥ 2 and y ≥  3 then x+y > 5. A) True,  B) False.

B.

9. The bound  x < 9 is sharper than  x < 9.5.  A) True,  B) False.

A.

10. 1 =  0 provided that 0 = 0.   A) True,  B) False.

B.

11. x > 0 or  y > 0 only if  xy ≥ 0.   A) True,  B) False

B.

12. x ≥ 2 provided that x = 2.   A) True , B) False.

A.

13. The linear program given by a  standard tableau with the matrix

 -1 2 0 -3 0 -4 0 -2 0 0 0 -1 0 2 -3

(A) is infeasible, (B) is unbounded,  (C) has an optimal solution,

(D) has only 2 linear constraints.

B.

14. The linear program given by a  standard tableau with the matrix

 -1 -2 -1 3 0 -4 0 2 0 1 0 1 1 1 -3

(A) is infeasible, (B) is unbounded, (C) has an optimal solution,

(D) requires at least two pivot steps to solve by simplex method.

C.

15. The linear program given by a  standard tableau with the matrix

 -1 -2 0 -3 -1 -4 0 2 0 1 -1 1 0 2 -3

(A) is infeasible, (B) is unbounded, (C) has an optimal solution,

(D) has -3 as the optimal value.

A.

16. The standard tableau

x1 x2 x3  1

0    0   0  -1 = x4

0   -2   3   4 -> min

(A) is optimal, (B) has a bad column, (C) has a bad row, (D) is not standard.

B, C.

17.  For any numbers a, b, and c. the standard tableau

1

-a = x1

-b= x2

-c -> min

(A) is optimal. (B) has a bad column, (C) has a bad row, (D) is  terminal.

D.

18. Pivoting the standard tableau with matrix

2*  3

-4   3

produces a tableau which

(A) is optimal,  (B)  has a bad row,  (C) has a bad column,  (D) is not terminal.

D.

19. Pivoting the standard tableau with matrix

1   2*  -3

2   4     3

produces a tableau which

(A) is optimal,  (B)  has a bad row,  (C) has a bad column,  (D) is not terminal.

A.

20. The linear program x+y -> max, x≤  -2, x  ≤ - 1 with 2 unknowns x, y

A) is infeasible. B) is unbounded. C) has an optimal solution.

D) has infinitely many optimal solutions.

B.

21. The number of choices for the pivot entry in the standard tableau with the matrix

-1   2   -3    -1      0   1

0  -1    -1    -3     -3  3

-1  -1   -2   -3     -4   3

which are consistent with the simplex method is  (A) 0, (B) 2, (C)  4, (D) 6.

D.

22. The number of choices for the pivot entry in the standard tableau with the matrix

-1   2   -3    -1      0   1

0  -1    -1    -3     3   3

-1  -1   -2    -3    -4   3

which are consistent with the simplex method is  (A) 0, (B) 2, (C)  4, (D) 6.

A.

23. The number of choices for the pivot entry in the standard tableau with the matrix

1  - 2    3    -1    1

0  -1    1      3    1

1  -1    2     -3    4

which are consistent with the simplex method.is  (A) 0, (B) 1, (C )  2, (D) 3.

C.

24. The linear program given by  the row tableau  with  x1,  x3, x4, x5  ≥ 0

x1             2 x1        - x3         1

 -1 -2 0 -3 = -x4 -4 0 -2 0 = x5 0 1 1 2 -> min

(A) is infeasible, (B) is unbounded,  (C) has an optimal solution,

(D) has only 2 linear constraints.

B.

25. The set of constraints x + y ≥ 2, 2x + 3y ≥  4 implies that

A) 4x + 5y >  8,  B) x > 0,   C) y > 1,   D)  x + y > 0.

D.