Kilgore's Dell is a small delicatessen located near a major university. Kilgore's does a large walk-in carry-out lunch business. The deli offers two luncheon chili specials, Wimpy and Dial 911. At the beginning of the day, Kilgore needs to decide how much of each special to make (he always sells out of whatever he makes). The profit on one serving of Wimpy is $0.43, on one serving of Dial 911, $0.56. Each serving of Wimpy requires 0.23 pound of beef, 0.23 cup of onions, and 5 ounces of Kilgore's special sauce. Each serving of Dial 911 requires 0.23 pound of beef, 0.38 cup of onions, 2 ounces of Kilgore's special sauce, and 5 ounces of hot sauce. Today, Kilgore has 18 pounds of beef, 13 cups of onions, 87 ounces of Kilgore's special sauce, and 58 ounces of hot sauce on hand. a. Develop a linear programming model that will tell Kilgore how many servings of Wimpy and Dial 911 to make in order to maximize his profit today. If required, round your answers to two decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) Let W = number of servings of Wimpy to make D = number of servings of Dial 911 to make Max W+ s.t. W+ (Beef) W+ (Onions) W+ (Special Sauce) W+ (Hot Sauce) W, D D D D D 2 0
Kilgore's Dell is a small delicatessen located near a major university. Kilgore's does a large walk-in carry-out lunch business. The deli offers two luncheon chili specials, Wimpy and Dial 911. At the beginning of the day, Kilgore needs to decide how much of each special to make (he always sells out of whatever he makes). The profit on one serving of Wimpy is $0.43, on one serving of Dial 911, $0.56. Each serving of Wimpy requires 0.23 pound of beef, 0.23 cup of onions, and 5 ounces of Kilgore's special sauce. Each serving of Dial 911 requires 0.23 pound of beef, 0.38 cup of onions, 2 ounces of Kilgore's special sauce, and 5 ounces of hot sauce. Today, Kilgore has 18 pounds of beef, 13 cups of onions, 87 ounces of Kilgore's special sauce, and 58 ounces of hot sauce on hand. a. Develop a linear programming model that will tell Kilgore how many servings of Wimpy and Dial 911 to make in order to maximize his profit today. If required, round your answers to two decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) Let W = number of servings of Wimpy to make D = number of servings of Dial 911 to make Max W+ s.t. W+ (Beef) W+ (Onions) W+ (Special Sauce) W+ (Hot Sauce) W, D D D D D 2 0
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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![### Optimization and Shadow Pricing in Linear Programming
**b. Find an optimal solution.**
- If required, round your answers to two decimal places.
\[ \begin{align*}
W &= \_\_\_\_ \\
D &= \_\_\_\_ \\
\text{Profit} &= \$\_\_\_\_
\end{align*} \]
**c. What is the shadow price for special sauce?**
- If required, round your answers to two decimal places.
\[ \text{\$} \_\_\_\_ \]
Interpret the shadow price.
*Note: The input in the box below will not be graded, but may be reviewed and considered by your instructor.*
\[ \begin{minipage}{\linewidth}
\vspace{40px}
\end{minipage} \]
**d. Increase the amount of special sauce available by 1 ounce and re-solve.**
- If required, round your answers to two decimal places.
\[ \begin{align*}
W &= \_\_\_\_ \\
D &= \_\_\_\_ \\
\text{Profit} &= \$\_\_\_\_
\end{align*} \]
Does the solution confirm the answer to part (c)?
---
This material covers exercises in optimization problems and shadow pricing in the context of linear programming. Follow the instructions and input the required values as accurately as possible. Your responses will help in understanding the concepts of optimal solutions and shadow pricing, which are critical in resource allocation and economic modeling.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8665c90a-e228-4cf6-bf60-57dab8fd52d5%2F43c12b04-f2b1-4a32-b5c8-b26b88432697%2Ftdcts1_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Optimization and Shadow Pricing in Linear Programming
**b. Find an optimal solution.**
- If required, round your answers to two decimal places.
\[ \begin{align*}
W &= \_\_\_\_ \\
D &= \_\_\_\_ \\
\text{Profit} &= \$\_\_\_\_
\end{align*} \]
**c. What is the shadow price for special sauce?**
- If required, round your answers to two decimal places.
\[ \text{\$} \_\_\_\_ \]
Interpret the shadow price.
*Note: The input in the box below will not be graded, but may be reviewed and considered by your instructor.*
\[ \begin{minipage}{\linewidth}
\vspace{40px}
\end{minipage} \]
**d. Increase the amount of special sauce available by 1 ounce and re-solve.**
- If required, round your answers to two decimal places.
\[ \begin{align*}
W &= \_\_\_\_ \\
D &= \_\_\_\_ \\
\text{Profit} &= \$\_\_\_\_
\end{align*} \]
Does the solution confirm the answer to part (c)?
---
This material covers exercises in optimization problems and shadow pricing in the context of linear programming. Follow the instructions and input the required values as accurately as possible. Your responses will help in understanding the concepts of optimal solutions and shadow pricing, which are critical in resource allocation and economic modeling.
![## Optimizing Luncheon Special Production at Kilgore's Deli
**Introduction:**
Kilgore's Deli is a small delicatessen located near a major university, specializing in carry-out lunch business. The deli offers two luncheon chili specials: Wimpy and Dial 911. Kilgore needs to determine the optimal number of each special to prepare each day to maximize his profit, always selling out his daily production.
**Profit Values:**
- Profit per serving of Wimpy: $0.43
- Profit per serving of Dial 911: $0.56
**Ingredient Requirements:**
Each serving of Wimpy requires:
- 0.23 pounds of beef
- 0.23 cups of onions
- 5 ounces of Kilgore's special sauce
Each serving of Dial 911 requires:
- 0.23 pounds of beef
- 0.38 cups of onions
- 2 ounces of Kilgore's special sauce
- 5 ounces of hot sauce
**Available Ingredients:**
- Beef: 18 pounds
- Onions: 13 cups
- Kilgore's special sauce: 87 ounces
- Hot sauce: 58 ounces
### Problem Statement:
Develop a linear programming model to determine the number of servings of Wimpy and Dial 911 to make for maximizing profit.
### Linear Programming Model:
**Let:**
- \( W \) = Number of servings of Wimpy to make
- \( D \) = Number of servings of Dial 911 to make
**Objective Function:**
\[ \text{Maximize} \quad 0.43W + 0.56D \]
**Subject to the Constraints:**
1. Beef constraint:
\[ 0.23W + 0.23D \leq 18 \quad \text{(Beef)} \]
2. Onions constraint:
\[ 0.23W + 0.38D \leq 13 \quad \text{(Onions)} \]
3. Special sauce constraint:
\[ 5W + 2D \leq 87 \quad \text{(Special Sauce)} \]
4. Hot sauce constraint:
\[ 5D \leq 58 \quad \text{(Hot Sauce)} \]
5. Non-negativity constraints:
\[ W, D \geq 0 \]
### Tabular Representation:
Maximize
\[](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8665c90a-e228-4cf6-bf60-57dab8fd52d5%2F43c12b04-f2b1-4a32-b5c8-b26b88432697%2Fme1vfmw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Optimizing Luncheon Special Production at Kilgore's Deli
**Introduction:**
Kilgore's Deli is a small delicatessen located near a major university, specializing in carry-out lunch business. The deli offers two luncheon chili specials: Wimpy and Dial 911. Kilgore needs to determine the optimal number of each special to prepare each day to maximize his profit, always selling out his daily production.
**Profit Values:**
- Profit per serving of Wimpy: $0.43
- Profit per serving of Dial 911: $0.56
**Ingredient Requirements:**
Each serving of Wimpy requires:
- 0.23 pounds of beef
- 0.23 cups of onions
- 5 ounces of Kilgore's special sauce
Each serving of Dial 911 requires:
- 0.23 pounds of beef
- 0.38 cups of onions
- 2 ounces of Kilgore's special sauce
- 5 ounces of hot sauce
**Available Ingredients:**
- Beef: 18 pounds
- Onions: 13 cups
- Kilgore's special sauce: 87 ounces
- Hot sauce: 58 ounces
### Problem Statement:
Develop a linear programming model to determine the number of servings of Wimpy and Dial 911 to make for maximizing profit.
### Linear Programming Model:
**Let:**
- \( W \) = Number of servings of Wimpy to make
- \( D \) = Number of servings of Dial 911 to make
**Objective Function:**
\[ \text{Maximize} \quad 0.43W + 0.56D \]
**Subject to the Constraints:**
1. Beef constraint:
\[ 0.23W + 0.23D \leq 18 \quad \text{(Beef)} \]
2. Onions constraint:
\[ 0.23W + 0.38D \leq 13 \quad \text{(Onions)} \]
3. Special sauce constraint:
\[ 5W + 2D \leq 87 \quad \text{(Special Sauce)} \]
4. Hot sauce constraint:
\[ 5D \leq 58 \quad \text{(Hot Sauce)} \]
5. Non-negativity constraints:
\[ W, D \geq 0 \]
### Tabular Representation:
Maximize
\[
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