Math 484.2   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 ≤ 2, x    3

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

27. For every  t, the equation    sin(t)  = ty   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  0*  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=1, y = 0, z = 0, u = 2 is (A) a feasible solution, (B) an optimal solution,(C) the basic solution.

32. The optimal value of the   program   x+ty 3-> min, x2  1,   y2 ≤ 1

as a function of the parameter  t  has the following slopes: (A) 8, -8, (B) 1,(C) 1,-1, (D) -1, 0.

33. The optimal value of the   program   x+y -> max, |x| ≤ t+1,   |y| ≤ 2t

as a function of the parameter  t  has the following slopes: (A) -3, (B) 3,(C) -3, 3.

34. The optimal value of the  job assignment problem

 3 1 3 1 2 1 3 1 3 2 2 2 3 3 5 3 4 2 3 2 4 2 2 2 1 1 3 1 3 1 2 2 2 1 1 1

is (A) < 8, (B)  8,  (C) > 8.

35. The optimal value  for the transportation problem

 2 1 3 2 1 2 1 2 1 9 1 2 2 1 1 2 1 3 1 8 2 2 1 3 1 1 3 1 2 9 0 5 1 1 2 1 2 3 0 8 6 1 6 1 6 1 6 1 6 demand\supply

is (A) < 25 (B) 25, (C) > 25.