Again, linear programming algorithms correctly detect when this case occurs. 3.The optimal solution need not be unique, as a \side" of the feasible region might be parallel to the levels sets of the objective function. Whenever the feasible region is bounded, however, there always exists an optimal solution that is a vertex of the feasible region.4 Consider the following linear programming problem: Min s.t. X,+2x2 X, +3 x 90 8x,+2x, 2160 3x, +2x, 2120 X,570 *1,*,20 a. Write the problem in standard form. Identify slack/surplus variables. (10 points) b. The optimal solution of the above LP model is (180/7, 150/7). Systems of inequalities are used when a problem requires a range of solutions, and there is more than one constraint on those solutions. As with the example above, systems of inequalities are often used to define the constraints on a solution. When a problem requires you to pick an optimal solution, then this requires linear programming or ...