Please someone answer this if you actually know about operations research For ea
ID: 3209810 • Letter: P
Question
Please someone answer this if you actually know about operations research
For each of the following linear programming models below, which is the more efficient way to obtain an optimal solution: by applying the simplex method directly to this primal problem or by applying the simplex method directly to the dual problem instead. Explain why. (a) Maximize Z=10x1-4x2+7x3, subject to 3x, - x2 + 2r3 S 25 x1-2x2 + 3x3 25 5x + x2 + 2x3 S 40 and 20 (b) Maximize Z = 2x1 + 5x2 + 3x3 + 4x4 + x5, subject to x +3x2 2x3 3x4 +xs S 6 4x6x2 + 5x3 + 7x4 + x5 s 15 and x, 0, for j 1, 2, 3, 4, 5.Explanation / Answer
First note that the number of constraints in primal is equal to number of variables in the dual and vice versa. So, it is computational advantage if we convert an LPP (linear programming problem) with more constraints and less variables into its dual and solve it. Because the dual will have less number of constraints and hence less number of basic variables. so in these cases, the number of computations will be reduced by solving the dual instead of primal directly.
Problem (a) contains more constraints and less number of variables. So it is advantageous to convert the problem into dual and solve the dual. because the dual will have less constraints and easy to solve.
If we convert problem (b) into dual then the number of constraints in dual will be increased and consequently the number of basic varibales also. This leads to more comutations. So, it is better to solve the primal directly with out converting into dual