Question: Given the following LP and its optimal solution: max z - 5x1 + 12x2 + 3x3 Optimal Solution: st 4x1 + 2x2 + 2x3 s

Given the following LP and its optimal solution: max z - 5x1 + 12x2 + 3x3 Optimal Solution: st 4x1 + 2x2 + 2x3 s 20 xg" - [s1, x2,53] 5x + 9x2 + 4x3 $30 z = 40 B1. (1.-2/9,0 1x: + 0x2 + 1x3 5 6 X1, X2, X3 20 0, 1/9,0 0,0,1) a) Complete ONE of the following. 1. How much can the objective function coefficient of x2, cx2, change without changing the optimal solution? 2. How much can the right hand side of the second constraint, b2, change without changing the optimal solution? 3. If we add a new variable, x4, with the following data, would the optimal solution change? CX4 - 10 Ax4T -(1,2,0] b) Formulate the dual of the given LP c) Use the rules of complementary slackness to find the optimal solution to the dual problem. Clearly identify all of the dual variable values, the slack or excess variable values, and the objective function value

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