Maximize P = <24 <32 subject to
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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All one questions please help finite math
![**Problem Statement:**
Discount Tire Center has $14,879 available per month for advertising. Newspaper ads cost $240 each and can occur a maximum of 24 times per month. Radio ads cost $600 each and can occur a maximum of 32 times per month at this price. Each newspaper ad reaches 7,000 men in the target group, and each radio ad reaches 8,500 of these men. The company wants to maximize the number of ad exposures to the target group.
**Variables and Objective:**
- Use \( N \) for the number of newspaper advertisements.
- Use \( R \) for the number of radio advertisements.
Maximize \( P = \) [Formula for maximizing exposures], subject to the following constraints:
1. \( N \leq 24 \)
2. \( R \leq 32 \)
3. \( 240N + 600R \leq 14,879 \)
**Instructions:**
Enter the solution to the simplex matrix below. If there is no solution, enter 'DNE' in the boxes. If more than one solution exists, enter only one of the multiple solutions. Round all answers to the nearest whole if needed.
- Number of Newspaper ads to run is: [ ]
- Number of Radio ads to run is: [ ]
- Maximum target group exposure is: [ ]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F410204a0-8764-4473-a9c2-14bad68c17f5%2F141940d5-17a1-492d-913c-1770bec731d2%2Fcgc77or_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Discount Tire Center has $14,879 available per month for advertising. Newspaper ads cost $240 each and can occur a maximum of 24 times per month. Radio ads cost $600 each and can occur a maximum of 32 times per month at this price. Each newspaper ad reaches 7,000 men in the target group, and each radio ad reaches 8,500 of these men. The company wants to maximize the number of ad exposures to the target group.
**Variables and Objective:**
- Use \( N \) for the number of newspaper advertisements.
- Use \( R \) for the number of radio advertisements.
Maximize \( P = \) [Formula for maximizing exposures], subject to the following constraints:
1. \( N \leq 24 \)
2. \( R \leq 32 \)
3. \( 240N + 600R \leq 14,879 \)
**Instructions:**
Enter the solution to the simplex matrix below. If there is no solution, enter 'DNE' in the boxes. If more than one solution exists, enter only one of the multiple solutions. Round all answers to the nearest whole if needed.
- Number of Newspaper ads to run is: [ ]
- Number of Radio ads to run is: [ ]
- Maximum target group exposure is: [ ]
![**Problem Statement: Maximizing Profit for Sweet-Fit Jeans Factory**
Sweet-Fit jeans has a factory that produces two styles of jeans: Super-Fit and Super-Hug. Below are the details of the production process and profit calculation for each style:
**Production Details:**
- **Super-Fit:**
- Cutting time: 12 minutes per pair
- Sewing and finishing time: 15 minutes per pair
- Profit per pair: $4.00
- **Super-Hug:**
- Cutting time: 12 minutes per pair
- Sewing and finishing time: 25 minutes per pair
- Profit per pair: $5.00
**Factory Constraints:**
- Maximum cutting time available per day: 10,799 minutes
- Maximum sewing and finishing time available per day: 16,499 minutes
**Objective:**
Determine the number of pairs of each style that should be produced daily to achieve the maximum profit.
**Mathematical Formulation:**
- Use \( x \) for Super-Fit and \( y \) for Super-Hug.
- The goal is to maximize the profit function \( P \):
\[ \text{Maximize } P = \quad \text{(to be calculated)} \]
**Constraints:**
1. Cutting time:
\[
12x + 12y \leq 10,799
\]
2. Sewing and finishing time:
\[
15x + 25y \leq 16,499
\]
**Solution Instructions:**
- Enter solutions for the simplex matrix calculations. If no solution exists, enter 'DNE' in the provided boxes.
- In case of multiple solutions, enter only one.
- Round the number of jeans to 1 decimal place and profits to 2 decimal places.
**Solution Input Fields:**
- Number of Super-Fit jeans to produce for maximum profit:
- **Number of Super-Fit:**
- **Profit:**
- Number of Super-Hug jeans to produce for maximum profit:
- **Number of Super-Hug:**
- **Profit:**
- **Maximum profit:**
- Enter the total maximum profit value.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F410204a0-8764-4473-a9c2-14bad68c17f5%2F141940d5-17a1-492d-913c-1770bec731d2%2Fnx2wd9j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement: Maximizing Profit for Sweet-Fit Jeans Factory**
Sweet-Fit jeans has a factory that produces two styles of jeans: Super-Fit and Super-Hug. Below are the details of the production process and profit calculation for each style:
**Production Details:**
- **Super-Fit:**
- Cutting time: 12 minutes per pair
- Sewing and finishing time: 15 minutes per pair
- Profit per pair: $4.00
- **Super-Hug:**
- Cutting time: 12 minutes per pair
- Sewing and finishing time: 25 minutes per pair
- Profit per pair: $5.00
**Factory Constraints:**
- Maximum cutting time available per day: 10,799 minutes
- Maximum sewing and finishing time available per day: 16,499 minutes
**Objective:**
Determine the number of pairs of each style that should be produced daily to achieve the maximum profit.
**Mathematical Formulation:**
- Use \( x \) for Super-Fit and \( y \) for Super-Hug.
- The goal is to maximize the profit function \( P \):
\[ \text{Maximize } P = \quad \text{(to be calculated)} \]
**Constraints:**
1. Cutting time:
\[
12x + 12y \leq 10,799
\]
2. Sewing and finishing time:
\[
15x + 25y \leq 16,499
\]
**Solution Instructions:**
- Enter solutions for the simplex matrix calculations. If no solution exists, enter 'DNE' in the provided boxes.
- In case of multiple solutions, enter only one.
- Round the number of jeans to 1 decimal place and profits to 2 decimal places.
**Solution Input Fields:**
- Number of Super-Fit jeans to produce for maximum profit:
- **Number of Super-Fit:**
- **Profit:**
- Number of Super-Hug jeans to produce for maximum profit:
- **Number of Super-Hug:**
- **Profit:**
- **Maximum profit:**
- Enter the total maximum profit value.
Expert Solution
Step 1 Introduction:-
Linear programming is a mathematical technique that is also used in operations management departments. This technique is commonly used to find the best outcome with the maximum profit. Linear programming has various methods; each method is chosen by the companies as per their requirements or based on different factors.
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