Given the following linear programming problem: max 4r1 +3r2+3+24 s.t. 4r1 +2r2+3+55 (1) 3z1 + 12...

 

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Given the following linear programming problem: max 4r1 +3r2+3+24 s.t. 4r1 +2r2+3+55 (1) 3z1 + 12 + 2ry +454 I1, 72, 13, 14 2 0 (2) Let s1, s2 denote the slack variables for the constraints (1) and (2), respectively. After applying the simplex algorithm, a portion of the final simplex tableau is as follows (12, 14 are basic variables, and RHS denotes Right-Hand Side): Basic 3 1 12 4 $1 82 RHS 1 -1 -1 2 (1) Identify and fill the missing mumbers in the final simplex tableau, without performing simplex iterations. Show your calculations. (2) What is the shadow price (dual optimal solution) for each of the constraints? (3) Suppose the coefficients of r, are changed from a14 021 to a14= 024 Is the current basic solution still feasible? Does it satisfy the optimality criterion? Show your steps. (Hint: find the new B, and check those two conditions separately). Given the following linear programming problem: max 4r1 +3r2+3+24 s.t. 4r1 +2r2+3+55 (1) 3z1 + 12 + 2ry +454 I1, 72, 13, 14 2 0 (2) Let s1, s2 denote the slack variables for the constraints (1) and (2), respectively. After applying the simplex algorithm, a portion of the final simplex tableau is as follows (12, 14 are basic variables, and RHS denotes Right-Hand Side): Basic 3 1 12 4 $1 82 RHS 1 -1 -1 2 (1) Identify and fill the missing mumbers in the final simplex tableau, without performing simplex iterations. Show your calculations. (2) What is the shadow price (dual optimal solution) for each of the constraints? (3) Suppose the coefficients of r, are changed from a14 021 to a14= 024 Is the current basic solution still feasible? Does it satisfy the optimality criterion? Show your steps. (Hint: find the new B, and check those two conditions separately).

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