ISyE 6669 Spring 2005 Mid-Term, Feb 24
1. (25 points) Consider the system of equations:
x1 - x2 - x3 = -4
x1 -3x2 = -6
(a) Does it have no solution, a unique solution, or an infinite number of solutions
(b) Plot the solution in 3 dimensions
Now add non-negativity constraints x1 > 0, x2 > 0, x3 > 0
(c) Plot the LP solution set (imposing the non-negativity constraints)
(d) Does the LP have an unbounded direction and if so, what is it?
2. (20 points) In the LP of problem (1.), suppose the objective is to minimize x1+
2x2+ x3. The optimum primal solution is x1 = 0, x2 = 2, x3 = 2. What is the optimum dual
solution? Plot the objective value vs. c1 where the current value of c1 = 1.
