Midterm 1 Oct 9, 2014 Math 484.002  25 questions, 3 pts each.

Name  Dr.V

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1. The equation ax +by = c for  x, y with given numbers a,b,c

(A) is not an equation, (B) is not linear,  (C) always have a solution, (D) always has infinitely many solutions.

2.   x = y     is

(A) a linear constraint for x, y,  (B) a linear inequality   for x, y,

(C) an affine function of x, y,  (D) an equation for x, y which cannot be solved,

3. The linear program  x+2y -> max subject to x+y = 1, x ≥ 0, y ≥ 0

(A) is unbounded,  (B) is infeasible,  (C)  has many optimal solutions, (D) has optimal value 2.

4. The optimal value for the linear program   ax + b  -> max, 0 ≤  x  ≤ 1  with an unknown  x and given numbers  a, b

(A)  it is not a linear program , (B)   is unbounded, (C) is a+ b,   (D) is b or a+b.

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

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

6. The mathematical program  x -> max,  x  ≤ 1

(A) is not a linear program, (B) is infeasible, (C) has an optimal solution,

(D) is unbounded.

7. The answer to the mathematical program   xy  -> min,  x+ y   =  8 is

(A) unbounded,  (B) infeasible,  (C) max = 16 at x = 4, y = 4,

(D) min =16 at x = 4, y = 4.

8. The minimal total time for the job assignment problem

3 2 1 0

3 0 2 1

2 5 3 0

0 1 2 1

is    (A) 0,  (B) 1,  (C) 2, (D) 3.

9. For each  number  t, the equation     (t-1)x= t2- 1  for unknown x

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

10. 0 = 2  if  0 = 1.   A) True,  B) False.

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

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

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

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

(D) has only 2 linear constraints.

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

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

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

(D) has only 2 linear constraints.

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

 -1 -2 -3 3 0 1 0 2 -6 -1 0 -1 0 -1 -3

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

(D) has only 2 linear constraints.

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

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

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

(D) has -4 as the optimal value.

16. The standard tableau

x1 x2 x3 1

0   0   0   -1 -> max

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

17. The standard tableau

1

1 = x1

0 = x2

-1 -> min

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

18. Pivoting the tableau

x     -y

2*   3 = -z

produces the tableau

A) z    -y                    B)  x         y                      C) x    y

1/2 -3/2 = -x                 2       -3/2 = z                  1/2  3 = z

19.The number of choices for the pivot entry in the standard tableau

1   2   3    -1    0

0  -1   1    -3   -3

1  -1   2    -3    4

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

20. The number of choices for the pivot entry in the standard tableau

1   2    -3    -1   0

0  -1     1    -3   3

-1  -1   -2     3   4

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

21.The system x+ 2y = 3, 4x + 8y = 12  for x,y

(A) has no solutions, (B) has exactly one solution, (C) has infinitely many solutions.

22.  For any  row   x = [a, b]    of numbers,    x ≥ 0 or -x ≥ 0  provided that 0 = 0   A) True  B) False

23. The linear program given by the row tableau

a  -b   c     -d  -3

1  - 2   3    -1   0   = e

0  -1    1    -3   0 =  -f

1  -1    2    -3   4 -> min

with 6 unknowns  a,b,c,d,e,f ≥ 0  has optimal value

(A) 12,  (B) -4/3,  (C) , (D) -∞.

24.  For any number  x,  if    0 = 0  then    x ≥ 0 or x ≤ 0.     A) True   B) False

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

A) 4x + 5y ≥  9,  B) x ≥ 2,   C) y ≥ 1,   D) x ≤ 0.