Question: 1. Consider the following linear programming problem minimise Z =1I -212 subject to -21 - 12 2 -3 - TI + 12 2-1 T1 20,

1. Consider the following linear programming problem minimise Z =1I -212 subject to -21 - 12 2 -3 - TI + 12 2-1 T1 20, 12 2 0. (a) Write the problem in standard form. (b) Solve the problem in standard form graphically. Also, . Introduce appropriate slack or surplus variables and define the boundaries of the feasible region in your graphical representation. . Indicate the shortest path to optimality. (c) Solve the problem manually using the simplex algorithm. Determine the optimal solution x* and the optimal value Z*. Explain every step you make. In particular: . How do you choose certain values to enter the basis? Explain why. . How do you choose which variables should leave the basis? Explain why. . How do you decide when to stop? Explain why

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