### Homework 4

Due in class, 1 March, 2012
- Given the following linear program: minimize -
*x*_{1} - *x*_{2}
subject to *x* being nonnegative and

*x*_{1} + *2x*_{2} ≤ 5

*x*_{1} ≤ 3

*x*_{2} ≤ 2

Find the feasible region and evaluate the objective function at the corners
to solve the program. Find the dual and do the same for the dual, verifying
that the primal and the dual have the same value.
- Using the same feasible region, repeat Exercise 1 for the objective function
*x*_{1} + *x*_{2}.
- Using the same feasible region, repeat Exercise 1 for the objective function
*-x*_{1}- 3*x*_{2}.
- ... more to be added later ...