Solutions to Assign 3 problems 1-5
Out of 45 points

1: (3pt)

Min: 1000 Tc + 2000 Cc + 3000 Ac + 1500 Tne + 3000 Cne + 3700 Ane
ST:  
Tc + Tne = 1000000
Cc + Cne = 1000000
Ac + Ane = 1000000
Tc + Cc + Ac =  800000
Tne + Cne + Ane = 2200000
All vars >= 0
(With appropriate assignment of variables).

2: (6pt)
x3 enters and x5 leaves giving a cost of -2

3: (6pt)
A) Q (0,3,0)
B) S = 3/7

4: (6pt)
 A = [2 1 1]
 b = 4
 c = [1 1 0]
 x_0 = [.1 .1 3.7]

 w = .00218
 z' = [.0996 .0998 -.008]
 z =  [.00996 .00998 -.03]
 x_1 = [1.283 1.286 0.148]

 w = .599
 z' = [-.254 .516 -.088]
 z  = [-.325 .664 -.013]
 x_2 = [.052 3.8 .098]

5) (6pt)
For each constraint B_i x <= d_i in T
Check if Ax <= b, B_i x >= d_i has a feasible solution.
If any do, then S is not properly contained in T.

Another pretty much equivalent way is to use B_i as a cost function 
and solve
  max B_i
  st  Ax <= b
for each i and see if the solution violates B_i xsol <= d_i

6,7,8) 6pt each