The following chart representing the feasible region of a ma

The following chart representing the feasible region of a math program is provided: Find the LP optimal solution (x1, x2) when OF = min Z when OF = Max Z Find the IP optimal solution (x1, x2). Find the optimal solution (x1, x2) by inspection, if this is a MIP with OF = min Z. when x1 integer and x2 continuous when x1 continuous and x2 binary

Solution

a) As Z, the OF, is increasing in the direction from left to right, the optimum solution when it is a maximization problem is at the feasible point B = (6.6,3.4), while when it is a minimization problem, the feasible point is D = (0,3.2).

b) For the IP, the maximization is achieved at the point B (again) while the minimization problem has optimum integer solution at the origin O = (0,0).

c) For the minimization problem, in both cases, when x1 is integer and x2 continuous, and when x1 is continous and x2 binary, the solution is at the origin itself.