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Questions and Answers
What is the objective function to maximize in the Flair Furniture Company problem?
What is the objective function to maximize in the Flair Furniture Company problem?
7T + 5C
What is the maximum number of chairs that Flair Furniture Company can produce?
What is the maximum number of chairs that Flair Furniture Company can produce?
450
What is the minimum number of tables that Flair Furniture Company must produce?
What is the minimum number of tables that Flair Furniture Company must produce?
100
Which of the following constraints represents the limitation on carpentry hours?
Which of the following constraints represents the limitation on carpentry hours?
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What is the profit per table?
What is the profit per table?
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In the first iteration, What is the final profit achieved by Flair Furniture Company?
In the first iteration, What is the final profit achieved by Flair Furniture Company?
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What is the final number of tables produced by Flair Furniture Company in the first iteration?
What is the final number of tables produced by Flair Furniture Company in the first iteration?
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What is the slack value for the carpentry hour constraint in the first iteration?
What is the slack value for the carpentry hour constraint in the first iteration?
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What is the slack value for the painting hour constraint in the first iteration?
What is the slack value for the painting hour constraint in the first iteration?
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What is the slack value for the maximum chair constraint in the first iteration?
What is the slack value for the maximum chair constraint in the first iteration?
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What is the slack value for the minimum table constraint in the first iteration?
What is the slack value for the minimum table constraint in the first iteration?
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What is the final profit achieved by Flair Furniture Company in the second iteration, where the right-hand side of the painting hour constraint is changed to $1,700$?
What is the final profit achieved by Flair Furniture Company in the second iteration, where the right-hand side of the painting hour constraint is changed to $1,700$?
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What is the final number of tables produced by Flair Furniture Company in the second iteration with the changed painting hour constraint?
What is the final number of tables produced by Flair Furniture Company in the second iteration with the changed painting hour constraint?
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What is the slack value for the carpentry hour constraint in the second iteration with the changed painting hour constraint?
What is the slack value for the carpentry hour constraint in the second iteration with the changed painting hour constraint?
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What is the slack value for the painting hour constraint in the second iteration with changed painting hours?
What is the slack value for the painting hour constraint in the second iteration with changed painting hours?
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What is the slack value for the maximum chair constraint in the second iteration with the changed painting hour constraint?
What is the slack value for the maximum chair constraint in the second iteration with the changed painting hour constraint?
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What is the slack value for the minimum table constraint in the second iteration with the changed painting hour constraint?
What is the slack value for the minimum table constraint in the second iteration with the changed painting hour constraint?
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What is the final profit achieved by Flair Furniture Company in the third iteration, where the coefficient of the table variable in the objective function is changed to $15$?
What is the final profit achieved by Flair Furniture Company in the third iteration, where the coefficient of the table variable in the objective function is changed to $15$?
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What is the final number of tables produced by Flair Furniture Company in the third iteration with the changed objective function coefficient?
What is the final number of tables produced by Flair Furniture Company in the third iteration with the changed objective function coefficient?
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What is the slack value for the carpentry hour constraint in the third iteration with the changed objective function coefficient?
What is the slack value for the carpentry hour constraint in the third iteration with the changed objective function coefficient?
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What is the slack value for the painting hour constraint in the third iteration with the changed objective function coefficient?
What is the slack value for the painting hour constraint in the third iteration with the changed objective function coefficient?
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What is the slack value for the maximum chair constraint in the third iteration with the changed objective function coefficient?
What is the slack value for the maximum chair constraint in the third iteration with the changed objective function coefficient?
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What is the slack value for the minimum table constraint in the third iteration with the changed objective function coefficient?
What is the slack value for the minimum table constraint in the third iteration with the changed objective function coefficient?
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What is the final profit achieved by Flair Furniture Company in the fourth iteration, where the coefficient of the chair variable in the objective function is changed to $8$?
What is the final profit achieved by Flair Furniture Company in the fourth iteration, where the coefficient of the chair variable in the objective function is changed to $8$?
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What is the final number of chairs produced by Flair Furniture Company in the fourth iteration with the changed objective function coefficient?
What is the final number of chairs produced by Flair Furniture Company in the fourth iteration with the changed objective function coefficient?
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Study Notes
Solver Results
- Solver found a solution (optimum) satisfying all constraints.
- Solution time was very quick (e.g., 0.016 seconds).
- Number of iterations was minimal (e.g., 3 subproblems).
Objective Cell (Max)
- Cell
$D$6represents profit. - Original profit value was $0.00.
- Final profit value achieved was $4,040.00.
- Objective was to maximize profit.
Variable Cells
- Cells
$B$5(Number of units Tables) and$C$5(Number of units Chairs) impact profit. - Initial values for Number of units Tables and Number of units Chairs were 0.
- The optimal values that maximized profit were 320 Tables and 360 Chairs.
Constraints
- Constraints limit production possible values
-
$D$10(Maximum Chairs): 360 <=450 chairs – Not Binding. -
$D$11(Minimum Tables): 320 >= 100 – Not Binding. -
$D$8(Carpentry Hours): 2400 <= 2,400 – Binding. -
$D$9(Painting Hours): 1000 <= 1,000 – Binding
Solver Options Details
- Max Time, max Sub problems, Precision all unlimited.
- Integer Tolerance 1 %
Slack
- These values indicate the unused capacity in constraints. (e.g, slack values of 90 and 220, representing unused capacity)
- Zero slack suggests the constraint was binding
Sensitivity Report (Multiple tables)
- Data for the effect of changes in profits on other constraints.
- Allowable Increase/ Decrease shows the range for changes in profit.
- Shadow Price for each constraint determines the effect of a minor change on the objective function.
LP Formulation
- Variables: T (Tables) & C (Chairs)
- Objective function: Maximize 7T + 5C (representing profit from tables and chairs)
- Constraints include carpentry hours, painting hours, maximum chairs, and minimum tables.
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Description
This quiz covers key concepts in optimization from operations research, focusing on maximizing profit through variable constraints. It highlights the use of solver tools and the impact of production constraints on profit outcomes. Test your understanding of optimization principles and their applications in real-world scenarios.
