Only need help with the sensitivity range **Sensitivity Analysis in Excel: Understanding the Range for Objective Function Coefficient**In sensitivity analysis, it is crucial to determine the range for which the coefficients of decision variables in the objective function can vary without altering the optimal solution. According to Excel's sensitivity report for the previously formulated model (Eagle Tavern), the sensitivity range for the objective function coefficient of $ x_3 $ (or Rainwater) is presented in the following options:1. $\boxed{\text{[1.25, } +\infty\text{]}}$2. $\boxed{\text{[1.5, } +\infty\text{]}}$3. $\boxed{\text{[-\infty, 1.5]}}$4. $\boxed{\text{[-\infty, 1.25]}}$Understanding these options is vital for decision-makers to anticipate how variations in the coefficient of $ x_3 $ could potentially impact the devised optimal strategy. #### Explanation of Options:- **Option 1: [1.25, +∞]** - This implies the coefficient of $ x_3 $ can range from 1.25 to positive infinity while maintaining the optimal solution.- **Option 2: [1.5, +∞]** - In this case, the coefficient of $ x_3 $ needs to be at least 1.5 but can increase indefinitely without affecting the optimal solution.- **Option 3: [-∞, 1.5]** - This suggests that the coefficient of $ x_3 $ can lie anywhere from negative infinity up to 1.5, ensuring that the same optimal solution holds.- **Option 4: [-∞, 1.25]** - Indicates that the coefficient of $ x_3 $ can go as low as negative infinity up to 1.25 without changing the optimality of the solution.Selecting the correct sensitivity range is essential in validating and ensuring the robustness of the formulated model's optimal solution against changes in the variable coefficients. **Planning for Super Bowl Sunday: Beer Stock Optimization Using Linear Programming**Betty Malloy, owner of the Eagle Tavern in Pittsburgh, is preparing for Super Bowl Sunday, and she must determine how much beer to stock. Betty stocks three brands of beer—Yodel, Shotz, and Rainwater. The cost per gallon (to the tavern owner) of each brand is shown in the table below. The tavern has a budget of $2,000 for beer for Super Bowl Sunday. Betty sells Yodel at a rate of $3.00 per gallon, Shotz at $2.50 per gallon, and Rainwater at $1.75 per gallon. Based on past football games, Betty has determined the maximum customer demand to be 400 gallons of Yodel, 500 gallons of Shotz, and 300 gallons of Rainwater. The tavern has the capacity to stock 1,000 gallons of beer; Betty wants to stock up completely.Betty wants to decide on the number of gallons of each brand of beer to order so as to make the most profit. Formulate a linear programming model for this problem. Define $ x_1 $ as the number of gallons of Yodel to order, $ x_2 $ as the number of gallons of Shotz to order, $ x_3 $ as the number of gallons of Rainwater to order, and $ Z $ as the total profit. Which of the following model formulations is correct?**Table: Beer Cost Per Gallon**| Brand | Cost/Gallon ||----------|--------------|| Yodel | $1.50 || Shotz | $0.90 || Rainwater| $0.50 |

Given: Betty stocks three brands of beer. The number of gallons of Yodel=x1 The number of gallons of…

Answered: According to Excel's sensitivity report…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Question

Only need help with the sensitivity range

**Sensitivity Analysis in Excel: Understanding the Range for Objective Function Coefficient**

In sensitivity analysis, it is crucial to determine the range for which the coefficients of decision variables in the objective function can vary without altering the optimal solution. According to Excel's sensitivity report for the previously formulated model (Eagle Tavern), the sensitivity range for the objective function coefficient of $ x_3 $ (or Rainwater) is presented in the following options:

1. $\boxed{\text{[1.25, } +\infty\text{]}}$
2. $\boxed{\text{[1.5, } +\infty\text{]}}$
3. $\boxed{\text{[-\infty, 1.5]}}$
4. $\boxed{\text{[-\infty, 1.25]}}$

Understanding these options is vital for decision-makers to anticipate how variations in the coefficient of $ x_3 $ could potentially impact the devised optimal strategy.

#### Explanation of Options:
- **Option 1: [1.25, +∞]**
- This implies the coefficient of $ x_3 $ can range from 1.25 to positive infinity while maintaining the optimal solution.
- **Option 2: [1.5, +∞]**
- In this case, the coefficient of $ x_3 $ needs to be at least 1.5 but can increase indefinitely without affecting the optimal solution.
- **Option 3: [-∞, 1.5]**
- This suggests that the coefficient of $ x_3 $ can lie anywhere from negative infinity up to 1.5, ensuring that the same optimal solution holds.
- **Option 4: [-∞, 1.25]**
- Indicates that the coefficient of $ x_3 $ can go as low as negative infinity up to 1.25 without changing the optimality of the solution.

Selecting the correct sensitivity range is essential in validating and ensuring the robustness of the formulated model's optimal solution against changes in the variable coefficients.

$**Planning for Super Bowl Sunday: Beer Stock Optimization Using Linear Programming** Betty Malloy, owner of the Eagle Tavern in Pittsburgh, is preparing for Super Bowl Sunday, and she must determine how much beer to stock. Betty stocks three brands of beer—Yodel, Shotz, and Rainwater. The cost per gallon (to the tavern owner) of each brand is shown in the table below. The tavern has a budget of $2,000 for beer for Super Bowl Sunday. Betty sells Yodel at a rate of $3.00 per gallon, Shotz at $2.50 per gallon, and Rainwater at $1.75 per gallon. Based on past football games, Betty has determined the maximum customer demand to be 400 gallons of Yodel, 500 gallons of Shotz, and 300 gallons of Rainwater. The tavern has the capacity to stock 1,000 gallons of beer; Betty wants to stock up completely. Betty wants to decide on the number of gallons of each brand of beer to order so as to make the most profit. Formulate a linear programming model for this problem. Define $ x_1 $ as the number of gallons of Yodel to order, $ x_2 $ as the number of gallons of Shotz to order, $ x_3 $ as the number of gallons of Rainwater to order, and $ Z $ as the total profit. Which of the following model formulations is correct? **Table: Beer Cost Per Gallon** | Brand | Cost/Gallon | |----------|--------------| | Yodel | $1.50 | | Shotz | $0.90 | | Rainwater| $0.50 |$

Transcribed Image Text:**Planning for Super Bowl Sunday: Beer Stock Optimization Using Linear Programming** Betty Malloy, owner of the Eagle Tavern in Pittsburgh, is preparing for Super Bowl Sunday, and she must determine how much beer to stock. Betty stocks three brands of beer—Yodel, Shotz, and Rainwater. The cost per gallon (to the tavern owner) of each brand is shown in the table below. The tavern has a budget of $2,000 for beer for Super Bowl Sunday. Betty sells Yodel at a rate of $3.00 per gallon, Shotz at $2.50 per gallon, and Rainwater at $1.75 per gallon. Based on past football games, Betty has determined the maximum customer demand to be 400 gallons of Yodel, 500 gallons of Shotz, and 300 gallons of Rainwater. The tavern has the capacity to stock 1,000 gallons of beer; Betty wants to stock up completely. Betty wants to decide on the number of gallons of each brand of beer to order so as to make the most profit. Formulate a linear programming model for this problem. Define $ x_1 $ as the number of gallons of Yodel to order, $ x_2 $ as the number of gallons of Shotz to order, $ x_3 $ as the number of gallons of Rainwater to order, and $ Z $ as the total profit. Which of the following model formulations is correct? **Table: Beer Cost Per Gallon** | Brand | Cost/Gallon | |----------|--------------| | Yodel | $1.50 | | Shotz | $0.90 | | Rainwater| $0.50 |

Expert Solution