5.1. Consider the LP problem from Example 5.1 and change its objective to: maximize 2= 21 + 22. Characterize the set of all optimal solutions.

FIGURE 5.1 A Two-Variable LP Problem Example 5.1 An LP Problem [Las70] Consider the following LP problem: maximizez=x1+3x2(or,minimizez=(x1+3x2))subjecttox1+x21x1+x22x1,x20. The solution set is depicted in Figure 5.1; it is the polyhedron bounded by the four straight lines: x2=0,x1+x2=2,x1+x2=1 and x1=0. Using graphical illustration, it is easy to see by moving upwards the objective function contour z=x1+3x2, that the optimal solution z is attained at the vertex x=(21,121)