A linear programming model is given as follows: Minimize Z= 5.2x + 2.5x + 6.0x3 Subject...

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A linear programming model is given as follows: Minimize Z= 5.2x₁ + 2.5x₂ + 6.0x3 Subject to 3x₁ + 2x₂ + 2x3 2 200 X₁ 20.4 iii. iv. V. x₁ + x₂ + x3 x₂ + x3 2x1 -≤ 0.2 x₁ = x₂ + x3 X1, X2, X3 20 (a) Solve the problem by using the computer. What are the minimum Z and the optimal point? (b) Obtain the values of the slack/surplus variables at the optimal solution in (a) (c) Identify the sensitivity range of the objective function coefficient of x₂. (d) Identify the sensitivity range of the value of the 1* resource constraint (right-hand side). (e) Identify the sensitivity range of the value of the 3rd resource constraint (right-hand side). (f) which of the following makes the model infeasible? (Choose one) i. ii. Increase of the coefficient of x, on the objective function to 2000 Decrease of the coefficient of x, on the 1st constraint to -5 Addition of a new constraint, x₁ + 2x₂ + 3x3 ≤ 100 Removal of the non-negativity constraints for X₁, X2, X3 None A linear programming model is given as follows: Minimize Z= 5.2x₁ + 2.5x₂ + 6.0x3 Subject to 3x₁ + 2x₂ + 2x3 2 200 X₁ 20.4 iii. iv. V. x₁ + x₂ + x3 x₂ + x3 2x1 -≤ 0.2 x₁ = x₂ + x3 X1, X2, X3 20 (a) Solve the problem by using the computer. What are the minimum Z and the optimal point? (b) Obtain the values of the slack/surplus variables at the optimal solution in (a) (c) Identify the sensitivity range of the objective function coefficient of x₂. (d) Identify the sensitivity range of the value of the 1* resource constraint (right-hand side). (e) Identify the sensitivity range of the value of the 3rd resource constraint (right-hand side). (f) which of the following makes the model infeasible? (Choose one) i. ii. Increase of the coefficient of x, on the objective function to 2000 Decrease of the coefficient of x, on the 1st constraint to -5 Addition of a new constraint, x₁ + 2x₂ + 3x3 ≤ 100 Removal of the non-negativity constraints for X₁, X2, X3 None

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Solving linear programming problems involves using optimization techniques to find the values of decision variables that minimize or maximize an objec... View the full answer