Mathematical modeling

solve the following problem using the graphical method. Compute the value of theobjective function and decision variables at optimality, and indicate which statementbest describes the solution: 1) this linear program has a unique optimnal solution, 2)this linear program has alternate optima, 3) this linear program is infeasible, or 4) thislinear program is unbounded.Minimize Z = 8x 1 + 4x 2Subject to 2x 1 – 2x 2 ≤ 24x 1 - 3x 2 ≥ -64x 1 + 2x 2 ≥ 84x 1 ≥ 44x 2 ≥ 6x 1 , x 2 ≥ 0SolutionThe graphical solution of Example 6 shows that it has alternate optimal solutions whichlie on the line segment between points B (1, 2) and C (1 .25, 1.5) with the objectivefunction equals 16 (optimal solution). It is noted that in this problem, if the objectivefunction is to be maximized, then the problem in this case is said to be unbounded as theobjective function line will move upward with no constraint to limit its movement.Systems Analysis 43 Dr. Emad Elbeltagi