Question: Consider the following LP. Maximize Z - -5x, + 5x2 + 13xy. subject to --X; + xy + 3x3 20 12x + 4xy + 10x

Consider the following LP. Maximize Z - -5x, + 5x2 + 13xy. subject to --X; + xy + 3x3 20 12x + 4xy + 10x 90 and * 0 (-1. 2. 3). If we let X and Xy be the stack variables for the respective con straints, the simplex method yields the following final set of equa- tions: (0) Z +213 +5 -100 (1) + + + 20 (2) lr - 26 - 444 + x - 10. a) b) (5 points) What is reduced cost of x? Explain what this value means (5 points) What is the range of the objective function coefficient of te for the current basis to remain optimal? (5 points) What is the new optimal solution if the objective function coefficient of changed from 5 to 8? State the optimal values of xs x and Z d) Consider the following LP. Maximize Z - -5x, + 5x2 + 13xy. subject to --X; + xy + 3x3 20 12x + 4xy + 10x 90 and * 0 (-1. 2. 3). If we let X and Xy be the stack variables for the respective con straints, the simplex method yields the following final set of equa- tions: (0) Z +213 +5 -100 (1) + + + 20 (2) lr - 26 - 444 + x - 10. a) b) (5 points) What is reduced cost of x? Explain what this value means (5 points) What is the range of the objective function coefficient of te for the current basis to remain optimal? (5 points) What is the new optimal solution if the objective function coefficient of changed from 5 to 8? State the optimal values of xs x and Z d)

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