Midterm 1 Oct 3, 2014 Math 484.003  25 questions, 2 pts each.

Name  Dr.V

No electronics is allowed.   Write both answers and details.

If you do not like given answers, write this and choose E on scantron.

Answers are in boldface Details are not given.

1. 2x -  1 ≠ -1   is

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

2.   x + y    0  is

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

(C) an affine function of x, y,  (D) an equation which can be solved,

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

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

4. The optimal value for the linear program   a2x + b  -> max, 0 ≤  x  ≤ 1  with an unknown  x and given numbers  a, b is

(A)  it is not a linear program , (B)   is unbounded, (C) a2 + b,   (D) b.

5. The mathematical program x/y -> max subject to |x| ≤ 1, y > 1 for 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  x2+ y2  -> min , x+ y     8 is

(A) max= 25  at x = 3,  y = 4,  (B) min = 0  at x = 0, y = 0 (C) max = 50 at x = 5, y =5,

(D) min =32 at x = 4, y = 4.

8. The minimal total time for the job assignment problem

3 2 1 4

3 0 2 1

2 5 3 6

0 1 2 1

is    (A) 4,  (B) 5,  (C) 6, (D) 7.

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

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

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

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

12. x > 0 only if x  ≥ 2.   A) True , B) False.

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

15. 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 -4 as the optimal value.

16. The standard tableau

x1 x2 x3 1

0   0   0   -1 -> min

(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 linear program x+y -> max, x≤  2, y ≤ - 1 with 2 unknowns x, y

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

D) has infinitely many optimal solutions.

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 is (A) 0, (B) 1, (C)  2, (D) 3.

21.The system x+ 2y = 3, 4x + 8y = 10  for x,y

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

22.  For any  column   x  of numbers,    0 = 0 implies that  x ≥ 0 or -x ≥ 0.   A) True  B) False

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

1  - 2   3    -1   0

0  -1   1    -3   0

1  -1   2    -3   4

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

24.  For any number  x,  if    x2 = 0 then     x ≥ 0 and 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 ≥ 0,   C) y ≥ 1,   D) x ≤ 0.