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Consider the following LP problem. Minimize z = 5x1 + 6x2+7x3, Subject to Constraint 1: 7x1 + 6x2 + 4x3 >= 50, Constraint 2: 10x1 + 13x2 + 14x3 >=150, Constraint 3: x1, x2, x3 >=0, where x1, x2, and x3 represent the decision variables. Solve the LP problem to answer the following questions. a-1. What are the values of x1, x2, and x3 at the optimal solution? Note: Round your answers to 2 decimal places. a-2. What is the minimum value of z? Note: Round your answers to 2 decimal places. b. Identify the binding and nonbinding constraints and report the surplus value, as appropriate. Note: If the answer to constraints is "Non-Binding" enter surplus value to 2 decimal places or leave cells blank. c. Report the values and ranges of feasibility of the shadow price of each binding constraint. Interpret the results. Note: Round your answers to 2 decimal places. d. What is the range of optimality for the three objective function coefficients? Interpret the results. Note: Round your answers to 2 decimal places.

Consider the following LP problem. Minimize z = 5x1 + 6x2+7x3, Subject to Constraint 1: 7x1 + 6x2 + 4x3 >= 50, Constraint 2: 10x1 + 13x2 + 14x3 >=150, Constraint 3: x1, x2, x3 >=0, where x1, x2, and x3 represent the decision variables. Solve the LP problem to answer the following questions. a-1. What are the values of x1, x2, and x3 at the optimal solution? Note: Round your answers to 2 decimal places. a-2. What is the minimum value of z? Note: Round your answers to 2 decimal places. b. Identify the binding and nonbinding constraints and report the surplus value, as appropriate. Note: If the answer to constraints is "Non-Binding" enter surplus value to 2 decimal places or leave cells blank. c. Report the values and ranges of feasibility of the shadow price of each binding constraint. Interpret the results. Note: Round your answers to 2 decimal places. d. What is the range of optimality for the three objective function coefficients? Interpret the results. Note: Round your answers to 2 decimal places.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the following LP problem. Minimize z = 5x1 + 6x2+7x3, Subject to Constraint 1: 7x1 + 6x2 + 4x3 >= 50, Constraint 2: 10x1 + 13x2 + 14x3 >=150, Constraint 3: x1, x2, x3 >=0, where x1, x2, and x3 represent the decision variables. Solve the LP problem to answer the following questions. a-1. What are the values of x1, x2, and x3 at the optimal solution? Note: Round your answers to 2 decimal places. a-2. What is the minimum value of z? Note: Round your answers to 2 decimal places. b. Identify the binding and nonbinding constraints and report the surplus value, as appropriate. Note: If the answer to constraints is "Non-Binding" enter surplus value to 2 decimal places or leave cells blank. c. Report the values and ranges of feasibility of the shadow price of each binding constraint. Interpret the results. Note: Round your answers to 2 decimal places. d. What is the range of optimality for the three objective function coefficients? Interpret the results. Note: Round your answers to 2 decimal places.
Transcribed Image Text:Consider the following LP problem. Minimize z = 5x1 + 6x2+7x3, Subject to Constraint 1: 7x1 + 6x2 + 4x3 >= 50, Constraint 2: 10x1 + 13x2 + 14x3 >=150, Constraint 3: x1, x2, x3 >=0, where x1, x2, and x3 represent the decision variables. Solve the LP problem to answer the following questions. a-1. What are the values of x1, x2, and x3 at the optimal solution? Note: Round your answers to 2 decimal places. a-2. What is the minimum value of z? Note: Round your answers to 2 decimal places. b. Identify the binding and nonbinding constraints and report the surplus value, as appropriate. Note: If the answer to constraints is "Non-Binding" enter surplus value to 2 decimal places or leave cells blank. c. Report the values and ranges of feasibility of the shadow price of each binding constraint. Interpret the results. Note: Round your answers to 2 decimal places. d. What is the range of optimality for the three objective function coefficients? Interpret the results. Note: Round your answers to 2 decimal places.
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