Home Work Set 1 MSIS 685, Linear Programming Fall 1998 Due : October 15 

Question 1 
Solve the following problem by the twophase simplex method (that is find an initial feasible dictionary and then using that solve to optimality. Show all intermediate dictionaries.

Question 2 
Consider the following dictionary:

Question 3 
Let C be a convex set which is both bounded and closed (that is it contains all of the points on its boundary. Prove that the set of all optimal points for the problem: is a convex set. 
Question 5 
Give an example of a linear program which is infeasible and its dual is also infeasible. 
Question 6 
For the problem in Question 1 write the dual problem and extract the optimal dual solution form the optimal dictionary. 
Question 7 
Find the dual of the following problem Then write down the complementary slackness relations between the primal and dual problems. 
Question 8 
Show that finding any feasible solution for a linear program in canonical form is equivalent to finding the optimal solution. To do so Prove that any optimal solution of is feasible for the system of inequalities and viceversa. 