1. 3 units.

You can send 2 units from s->a->b and 1 unit from s->b.
(You didn't need to explain this or describe the flow in your
quiz answer.)


2. 

maximize x_bt
subject to
  x_sa = s_ab
  x_ab + x_sb = x_bt
  0 <= x_sa <= 2
  0 <= x_sb <= 1
  0 <= x_ab <= 3
  0 <= x_bt <= 6

Or, you could have the same program as above, but where we maximize
x_sa + x_sb instead of maximizing x_bt.

Note that you cannot have max/min functions in the objective function
that you are maximizing.  For instance, you cannot write
  "maximize: min(x_bt, x_sb + min(x_sa, x_sb))".
That is not a linear function of the unknowns x_sa, x_ab, x_sb, x_bt,
and as a result it is not a linear program.  Also, it's important that
you express the objective function explicitly as a linear function of
the four variables x_sa, x_ab, x_sb, x_bt, and not just write something
like:
  "maximize: F(s,t), where F(s,t) is the amount of flow from s to t".
Many people had difficulty figuring out the right objective function.

If your answer involved residual graphs or iteratively finding paths
from s to t, then you are confusing the Ford-Fulkerson algorithm for
network flows (which does use those techniques) with linear programming
(which does not use those techniques).  This question asked about linear
programming.