hen a model has a unique optimal solution, it means that ________. A. the objective is...
hen a model has a unique optimal solution, it means that ________. A. the objective is maximized or minimized by more than one combination of decision variables B. there is no solution that simultaneously satisfies all the constraints C. the Allowable Increase or Allowable Decrease values for changing cells are zero D. there is exactly one solution that will result in the maximum or minimum objective
Homework Answers
The answer is
D. there is exactly one solution that will result in the maximum or minimum objective
Since the model has a unique optimal solution, Unique means one.
Hence, there is one solution which will achieve the objective.
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hen a model has a unique optimal solution, it means that
________. A. the objective is...
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...
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 The value of the objective function will not change The value of that decision variable will not change The value of slack or surplus variables for all constraints will be zero The dual value (shadow price) for every constraint will be...
Problem 3-12 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $69, 91, and $127, respe...
Problem 3-12 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $69, 91, and $127, respectively. The production requirements per unit are as follows: Number ofNumber of Manufacturing Fans Cooling Coils Time (hours) Economy 8 Standard 12 Deluxe 14 4 For the coming production period, the company has 200 fan motors, 340 cooling coils, and 2800 hours of manufacturing time available. How many economy models...
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...
Problem 3-12 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $67, $93, and $129,...
Problem 3-12 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $67, $93, and $129, respectively. The production requirements per unit are as follows: Number of Manufacturing Number of Cooling Coils Time (hours) Fans Economy Standard 12 Deluxe 14 For the coming production period, the company has 250 fan motors, 360 cooling coils, and 1800 hours of manufacturing time available. How many economy models (E),...
if you could only charge $18 for chairs, how is your optimal solution change? Variable Cells...
if you could only charge $18 for chairs, how is your optimal
solution change?
Variable Cells Allowable Increase Name Decision Variables X1 Decision Variables X2 Decision Variables X3 Final Value 2.0 0.0 8.0 Reduced Objective Cost Coefficient 0.0 60.0 -5.0 30.0 0.0 20.0 Allowable Decrease 20.0 4.0 5.0 1000000000000000000000000000000.0 2.5 5.0 Constraints Allowable Decrease Name Lumber bdft) Total Finishing (hrs) Total Carpentry (hrs) Total Tables demand (hrs) Final Value 24.0 20.0 8.0 0.0 Shadow Constraint Allowable Price R.H Side Increase...
questions 5 6 7 PARTILMULTIPLE CHOI how much or how many of something to produce, purchase, hire, etc. в, C. represent...
questions 5 6 7
PARTILMULTIPLE CHOI how much or how many of something to produce, purchase, hire, etc. в, C. represent the values of the constraints measure the objective function. D. must exist for each constraint. PNDVS 2. Which of the following statements is NOT true? A. A feasible solution satisfies all constraints. B. An optimal solution satisfies all constraints. C An infeasible solution violates all constraints. D. A feasible solution point does not have to lie on the boundary...
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...
Problem 3-12 (Algorithmic) uality Air Conditioning manufactures three home air conditioners: an economy mode a standard model and a deluxe mo e The profits per nit are S,, 4 , and respectively. The p...
Problem 3-12 (Algorithmic) uality Air Conditioning manufactures three home air conditioners: an economy mode a standard model and a deluxe mo e The profits per nit are S,, 4 , and respectively. The production requirements per unit are as follows: Number of Number of Manufacturing Cooling Coils Time (hours) Fans Economy 8 Standard 12 Deluxe 4 14 For the coming production period, the company has 320 fan motors, 380 cooling coils, and 3200 hours of manufacturing time available. How many...
(b) A LP model and its solution outputs and sensitivity report are as below. LP Model: Maximise R 7X+5Y+10 Z Subjective to: CI: 2X +Y+32 <= 50 C3: X 3 C6: X, Y, Z)so Outputs & Sensitivity Repo...
(b) A LP model and its solution outputs and sensitivity report are as below. LP Model: Maximise R 7X+5Y+10 Z Subjective to: CI: 2X +Y+32 <= 50 C3: X 3 C6: X, Y, Z)so Outputs & Sensitivity Report: Objective Cell Name Valu 101.33 SC$8 Max Variable Cells Final Value ReducedObjective Allowable Allowable Coefficient Increase Cell Name Cost Decrease 7.333333333 SC$3 X 0 E+30 SC$4 Y 0 5 4.333333333 E+30 SC$5 2 4 0 10 1.666666667 E+30 Constraints Final Value Shadow...
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...
Problem 3-12 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $69, 91, and $127, respectively. The production requirements per unit are as follows: Number ofNumber of Manufacturing Fans Cooling Coils Time (hours) Economy 8 Standard 12 Deluxe 14 4 For the coming production period, the company has 200 fan motors, 340 cooling coils, and 2800 hours of manufacturing time available. How many economy models...
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...
Problem 3-12 (Algorithmic) Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $67, $93, and $129, respectively. The production requirements per unit are as follows: Number of Manufacturing Number of Cooling Coils Time (hours) Fans Economy Standard 12 Deluxe 14 For the coming production period, the company has 250 fan motors, 360 cooling coils, and 1800 hours of manufacturing time available. How many economy models (E),...
if you could only charge $18 for chairs, how is your optimal
solution change?
Variable Cells Allowable Increase Name Decision Variables X1 Decision Variables X2 Decision Variables X3 Final Value 2.0 0.0 8.0 Reduced Objective Cost Coefficient 0.0 60.0 -5.0 30.0 0.0 20.0 Allowable Decrease 20.0 4.0 5.0 1000000000000000000000000000000.0 2.5 5.0 Constraints Allowable Decrease Name Lumber bdft) Total Finishing (hrs) Total Carpentry (hrs) Total Tables demand (hrs) Final Value 24.0 20.0 8.0 0.0 Shadow Constraint Allowable Price R.H Side Increase...
questions 5 6 7
PARTILMULTIPLE CHOI how much or how many of something to produce, purchase, hire, etc. в, C. represent the values of the constraints measure the objective function. D. must exist for each constraint. PNDVS 2. Which of the following statements is NOT true? A. A feasible solution satisfies all constraints. B. An optimal solution satisfies all constraints. C An infeasible solution violates all constraints. D. A feasible solution point does not have to lie on the boundary...
Problem 3-12 (Algorithmic) uality Air Conditioning manufactures three home air conditioners: an economy mode a standard model and a deluxe mo e The profits per nit are S,, 4 , and respectively. The production requirements per unit are as follows: Number of Number of Manufacturing Cooling Coils Time (hours) Fans Economy 8 Standard 12 Deluxe 4 14 For the coming production period, the company has 320 fan motors, 380 cooling coils, and 3200 hours of manufacturing time available. How many...
(b) A LP model and its solution outputs and sensitivity report are as below. LP Model: Maximise R 7X+5Y+10 Z Subjective to: CI: 2X +Y+32 <= 50 C3: X 3 C6: X, Y, Z)so Outputs & Sensitivity Report: Objective Cell Name Valu 101.33 SC$8 Max Variable Cells Final Value ReducedObjective Allowable Allowable Coefficient Increase Cell Name Cost Decrease 7.333333333 SC$3 X 0 E+30 SC$4 Y 0 5 4.333333333 E+30 SC$5 2 4 0 10 1.666666667 E+30 Constraints Final Value Shadow...
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