Question: 2. (Dual simplex, Graphical solution method). Consider the following LP. (min)f(x) = 5x + 4x2 = s.t. X1 + 12 - X3 = 1 Il-72

2. (Dual simplex, Graphical solution method).

2. (Dual simplex, Graphical solution method). Consider the following LP. (min)f(x) = 5x + 4x2 = s.t. X1 + 12 - X3 = 1 Il-72 - 24 = 5 X1,22, X3, X4 > 0. (a) Perform the dual simplex algorithm to find the optimal primal solution. 5+5+5=15 marks (b) Elliminate surplus variables r3 and 7a, to get the reduced equivalent model. 2 marks (c) Solve the following 2-dimensional LP problem by using the graphical so- lution method. 4 marks (min)f(x) = 5x1 + 4.22 s.t. x1 + x2 > 1 21-22 5 21, x2 > 0. (d) Assume that variables x; and 22 are integer in the previous model. Solve ILP problem by usling graphical solution method. 4 marks 2. (Dual simplex, Graphical solution method). Consider the following LP. (min)f(x) = 5x + 4x2 = s.t. X1 + 12 - X3 = 1 Il-72 - 24 = 5 X1,22, X3, X4 > 0. (a) Perform the dual simplex algorithm to find the optimal primal solution. 5+5+5=15 marks (b) Elliminate surplus variables r3 and 7a, to get the reduced equivalent model. 2 marks (c) Solve the following 2-dimensional LP problem by using the graphical so- lution method. 4 marks (min)f(x) = 5x1 + 4.22 s.t. x1 + x2 > 1 21-22 5 21, x2 > 0. (d) Assume that variables x; and 22 are integer in the previous model. Solve ILP problem by usling graphical solution method. 4 marks

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