Question 1 (Tuesday June 16)
There are two different trucks
and three routes
.
can only be used for the first two routes, while
can be used for all three,
so we have the decision variables (corresponding to edges):
These are all binary variables, that is:
The objective:
.
The constraints:
Question 2 (Wednesday, June 17)
Our problem here would be:
The LP relaxation is the same thing without the integer constraints:
And we computed in the previous homework that the solution to this is:
.
This isn't integer, so we branch into problem 2:
And problem 3:
These you can solve in your favourite method (I used a web solver) to get:
The solution for problem 2 is
, while problem 3 is infeasible. So, the optimal solution is the solution to problem 2,
.