Mathematical modeling

Minimize z = - 4x 1 - 6x 2Subject to - 4x 1 – 5x 2 ≤ - 10- x 1 - 4x 2 ≥ - 12- x 1 ≥ - 4x 2 ≥ 1x 1 , x 2 ≥ 015. Solve the following problem using the graphical method. Compute the value ofthe objective function and decision variables at optimality, and indicate whichstatement best describes the solution: 1) this linear program has a unique optimnalsolution, 2) this linear program has alternate optima, 3) this linear program isinfeasible, or 4) this linear program is unbounded.Minimize z = 10x 1 + 4x 2Subject to 5x 1 – 6x 2 ≤ 305x 1 +2x 2 ≥ 30x 1 ≥ 5x 2 ≥ 2.5x 1 , x 2 ≥ 016. Solve the following problem using the graphical method. Compute the value ofthe objective function and decision variables at optimality, and indicate whichstatement best describes the solution: 1) this linear program has a unique optimnalsolution, 2) this linear program has alternate optima, 3) this linear program isinfeasible, or 4) this linear program is unbounded.Maximize z = 24x 1 + 20x 2Subject to x 1 - x 2 ≥ -43x 1 - 2x 2 ≤ 6x 1 + x 2 ≥ 56x 1 + 5x 2 ≤ 10x 2 ≤ 6x 1 , x 2 ≥ 0Systems Analysis 49 Dr. Emad Elbeltagi