Given a linear programming optimal solution, if the value of the coefficient of a decision variable...
Given a linear programming optimal solution, if the value of the coefficient of a decision variable is changed but remains within its sensitivity range then
a linear programming optimal solution, if the value of the coefficient of a decision
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The value of the objective function will not change
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The value of that decision variable will not change
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The value of slack or surplus variables for all constraints will be zero
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The dual value (shadow price) for every constraint will be zero
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Both A and B
Homework Answers
Since, the value of the coefficient of a decision variable is changed but remains within its sensitivity range the value od objective function and decision variable will not change
Hence the correct answer is:
-
The value of the objective function will not change
-
The value of that decision variable will not change
or
both A and B
Add Answer to:
Given a linear programming optimal solution, if the value of the
coefficient of a decision variable...
Solve the following linear system using solver. Provide both the optimal solution and the optimal value...
Solve the following linear system using solver. Provide both the
optimal solution and the optimal value of the objective function at
the optimal solution.
Using the results you get in Excel, calculate the following (by
hand): Please show all work in excel.
Slack/surplus for every constraint.
Range of optimality for each decision variable.
Allowable increase (AI) and allowable decrease (AD) for each
decision variable.
max TO0x,x 2x +2x, S 16 B 20
True or False? 1. If an LP has multiple optimal solutions, then all solutions have the...
True or False? 1. If an LP has multiple optimal solutions, then all solutions have the same objective function value (such as total profit or cost). 2. As long as all prices (objective coefficients) change within their respective ranges, the optimal solution of a linear program does not change. 3. When a dual price changes within its range, the optimal solution does not change. 4. The solution of a linear program always consists of whole numbers (integers). That is why...
Match the following terms to their definition Feasible region Binding constraint [Choose] [Choose A feasible solution...
Match the following terms to their definition Feasible region Binding constraint [Choose] [Choose A feasible solution for which there are no other feasible points with a better objective function value in the entire feasible region. The change in the optimal objective function value per unit increase in the right-hand side of a constraint Restrictions that limit the settings of the decision variables A controllable input for a linear programming model The expression that defines the quantity to be maximized or...
Interpreting an LP output after solving the problem using the software. The following linear programming problem has been solved using the software. Use the output to answer the questi...
Interpreting an LP output after solving the problem using the software. The following linear programming problem has been solved using the software. Use the output to answer the questions below. LINEAR PROGRAMMING PROBLEM: MAX 25X1+30X2+15X3 S.T. 1) 4X1+5X2+8X3<1200 2) 9X1+15X2+3X3<1500 OPTIMAL SOLUTION: Objective Function Value = 4700.000 Variable Value Reduced Costs X1 140.000 0.000 X2 0.000 10.000 X3 80.000 0.000 Constraint Slack/Surplus Dual Prices 1 0.000 1.000 2 0.000 2.333 OBJECTIVE COEFFICIENT RANGES: Variable Lower Limit Current Value Upper Limit...
Consider the following linear programming problem Manimize $45X1 + $10X2 Subject To 15X1 + 5X2 2...
Consider the following linear programming problem Manimize $45X1 + $10X2 Subject To 15X1 + 5X2 2 1000 Constraint A 20X1 + 4X2 > 1200 Constraint B X1, X2 20 Constraint C if A and B are the two binding constraints. a) What is the range of optimality of the objective function? 3 C1/C2 s 5 b) Suppose that the unit revenues for X1 and X2 are changed to $100 and $15, respectively. Will the current optimum remain the same? NO...
. Consider a Linear Programming (LP) problem with two decision variables. If the profit (cost) coefficient...
. Consider a Linear Programming (LP) problem with two decision variables. If the profit (cost) coefficient of one decision variable of the objective function is increased, then a. The feasible region will be increased b. There will be a redundant constraint c. The slope of the profit (cost) line will be changed d. The feasible region will be decreased e. None of the above
Use this output to answer these questions please, I need to understand. Interpreting an LP output after solving the problem using the software. The following linear programming problem has been so...
Use this output to answer these questions please, I
need to understand.
Interpreting an LP output after solving the problem using the software. The following linear programming problem has been solved using the software. Use the output to answer the questions below LINEAR PROGRAMMING PROBLEM MAX 25x1+30x2+15x3 ST. 1) 4X1+5X2+8X3<1200 2) 9x1+15X2+3X3c1500 OPTIMAL SOLUTION: Objective Function Value- 4700.000 Variable Value 140.000 duced Costs 0.000 10.000 0.000 x1 x2 X3 0.000 80.000 Slack/Surplus 0.000 0.000 1.000 2.333 2 OBJECTIVE COEFFICIENT RANGES:...
S- In the optimal table of the simplex for the following linear programming problem x1, x3,...
S- In the optimal table of the simplex for the following linear programming problem x1, x3, are the basic variables. Min Z=-5X1+3X2+X3 X1+X2-X3<=10 X1+X2+X3<=60 What is the range for the first constraint right hand side for which the optimal table remains feasible? a. b. Is it profitable to increase a unit of resource for the 2nd constraint, if each unit of this resource is purchased for $2? What is the value of objective function and decision variables for this problem?...
1. Solving the linear programming problem Maximize z 3r1 2r2 3, subject to the constraints using ...
1. Solving the linear programming problem Maximize z 3r1 2r2 3, subject to the constraints using the simplex algorithm gave the final tableau T4 T5 #210 1-1/4 3/8-1/812 0 0 23/4 3/8 7/8 10 (a) (3 points) Add the constraint -221 to the final tableau and use the dual simplex algorithm to find a new optimal solution. (b) (3 points) After adding the constraint of Part (a), what happens to the optimal solution if we add the fourth constraint 2+...
a. What is the optimal solution in lay terms? What is the optimal value of the...
a. What is the optimal solution
in lay terms? What is the optimal value of the objective
function?
b. Which constraints are binding? Explain.
c. What are the shadow prices of demand for B constraint and
assembly time constraints? Interpret each.
d. If you could change the right-hand side of one constraint by
one unit (either increase or decrease), which one would you choose?
Why? Show all calculations.
e. State and interpret the ranges of optimality for any one of...
Solve the following linear system using solver. Provide both the
optimal solution and the optimal value of the objective function at
the optimal solution.
Using the results you get in Excel, calculate the following (by
hand): Please show all work in excel.
Slack/surplus for every constraint.
Range of optimality for each decision variable.
Allowable increase (AI) and allowable decrease (AD) for each
decision variable.
max TO0x,x 2x +2x, S 16 B 20
Match the following terms to their definition Feasible region Binding constraint [Choose] [Choose A feasible solution for which there are no other feasible points with a better objective function value in the entire feasible region. The change in the optimal objective function value per unit increase in the right-hand side of a constraint Restrictions that limit the settings of the decision variables A controllable input for a linear programming model The expression that defines the quantity to be maximized or...
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Use this output to answer these questions please, I
need to understand.
Interpreting an LP output after solving the problem using the software. The following linear programming problem has been solved using the software. Use the output to answer the questions below LINEAR PROGRAMMING PROBLEM MAX 25x1+30x2+15x3 ST. 1) 4X1+5X2+8X3<1200 2) 9x1+15X2+3X3c1500 OPTIMAL SOLUTION: Objective Function Value- 4700.000 Variable Value 140.000 duced Costs 0.000 10.000 0.000 x1 x2 X3 0.000 80.000 Slack/Surplus 0.000 0.000 1.000 2.333 2 OBJECTIVE COEFFICIENT RANGES:...
S- In the optimal table of the simplex for the following linear programming problem x1, x3, are the basic variables. Min Z=-5X1+3X2+X3 X1+X2-X3<=10 X1+X2+X3<=60 What is the range for the first constraint right hand side for which the optimal table remains feasible? a. b. Is it profitable to increase a unit of resource for the 2nd constraint, if each unit of this resource is purchased for $2? What is the value of objective function and decision variables for this problem?...
1. Solving the linear programming problem Maximize z 3r1 2r2 3, subject to the constraints using the simplex algorithm gave the final tableau T4 T5 #210 1-1/4 3/8-1/812 0 0 23/4 3/8 7/8 10 (a) (3 points) Add the constraint -221 to the final tableau and use the dual simplex algorithm to find a new optimal solution. (b) (3 points) After adding the constraint of Part (a), what happens to the optimal solution if we add the fourth constraint 2+...
a. What is the optimal solution
in lay terms? What is the optimal value of the objective
function?
b. Which constraints are binding? Explain.
c. What are the shadow prices of demand for B constraint and
assembly time constraints? Interpret each.
d. If you could change the right-hand side of one constraint by
one unit (either increase or decrease), which one would you choose?
Why? Show all calculations.
e. State and interpret the ranges of optimality for any one of...
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