Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. The firm has 700 hours of production time available in its cutting an sewing department, 400 hours available in its finishing department, and 200 hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table: Production Time (Hours) Cutting and Packaging and Model Sewing Finishing Shipping Profit/Glove Regular model 1 1/2 1/8 $5 Catcher's model 3/2 1 1/4 $8 Assuming that the company is interested in maximizing the total profit contribution, answer the following: (a) What is the linear programming model for this problem? If required, round your answers to 3 decimal places or enter your answers as a fraction. If the constant is "1" it must be entered in the box. Do not round intermediate calculation. If an amount is zero, enter "0". Let R = number of units of regular model. C = number of units of catcher's model. Маx R + s.t. R + Select your answer - v Cutting and Sewing R + C - Select your answer - v Finishing R + C - Select your answer - v Packing and Shipping R, C Select your answer - v
Kelson Sporting Equipment, Inc., makes two different types of baseball gloves: a regular model and a catcher's model. The firm has 700 hours of production time available in its cutting an sewing department, 400 hours available in its finishing department, and 200 hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table: Production Time (Hours) Cutting and Packaging and Model Sewing Finishing Shipping Profit/Glove Regular model 1 1/2 1/8 $5 Catcher's model 3/2 1 1/4 $8 Assuming that the company is interested in maximizing the total profit contribution, answer the following: (a) What is the linear programming model for this problem? If required, round your answers to 3 decimal places or enter your answers as a fraction. If the constant is "1" it must be entered in the box. Do not round intermediate calculation. If an amount is zero, enter "0". Let R = number of units of regular model. C = number of units of catcher's model. Маx R + s.t. R + Select your answer - v Cutting and Sewing R + C - Select your answer - v Finishing R + C - Select your answer - v Packing and Shipping R, C Select your answer - v
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
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![### Kelson Sporting Equipment, Inc.
Kelson Sporting Equipment, Inc., manufactures two types of baseball gloves: a regular model and a catcher's model. The company has specific production time limitations:
- **Cutting and Sewing Department:** 700 hours
- **Finishing Department:** 400 hours
- **Packaging and Shipping Department:** 200 hours
The table below details the production time required per glove and the profit contribution for each type of glove:
#### Production Time Requirements and Profit Contribution
| Model | Cutting and Sewing (Hours) | Finishing (Hours) | Packaging and Shipping (Hours) | Profit/Glove ($) |
|------------------|----------------------------|-------------------|-------------------------------|------------------|
| Regular model | 1 | 1/2 | 1/8 | 5 |
| Catcher's model | 3/2 | 1 | 1/4 | 8 |
#### Problem Statement
The objective is to maximize the total profit contribution. To achieve this, you need to develop a linear programming model.
#### Linear Programming Model
Let:
- \( R \) = number of units of regular model
- \( C \) = number of units of catcher's model
Maximize:
\[ \text{Profit} = \text{(Enter coefficient for R)} R + \text{(Enter coefficient for C)} C \]
Subject to:
1. Cutting and Sewing Constraint:
\[ \text{(Enter coefficient for R)} R + \text{(Enter coefficient for C)} C \leq 700 \]
2. Finishing Constraint:
\[ \text{(Enter coefficient for R)} R + \text{(Enter coefficient for C)} C \leq 400 \]
3. Packaging and Shipping Constraint:
\[ \text{(Enter coefficient for R)} R + \text{(Enter coefficient for C)} C \leq 200 \]
4. Non-negativity Constraints:
\[ R, C \geq 0 \]
The model will help determine the optimal production quantities of regular and catcher’s models to maximize profit while staying within the department time constraints.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6651891-800f-4769-b681-6d9b8aa30f6c%2Fd2e74ef4-544d-4277-8359-8b24283871bd%2Flbin5i_processed.png&w=3840&q=75)
Transcribed Image Text:### Kelson Sporting Equipment, Inc.
Kelson Sporting Equipment, Inc., manufactures two types of baseball gloves: a regular model and a catcher's model. The company has specific production time limitations:
- **Cutting and Sewing Department:** 700 hours
- **Finishing Department:** 400 hours
- **Packaging and Shipping Department:** 200 hours
The table below details the production time required per glove and the profit contribution for each type of glove:
#### Production Time Requirements and Profit Contribution
| Model | Cutting and Sewing (Hours) | Finishing (Hours) | Packaging and Shipping (Hours) | Profit/Glove ($) |
|------------------|----------------------------|-------------------|-------------------------------|------------------|
| Regular model | 1 | 1/2 | 1/8 | 5 |
| Catcher's model | 3/2 | 1 | 1/4 | 8 |
#### Problem Statement
The objective is to maximize the total profit contribution. To achieve this, you need to develop a linear programming model.
#### Linear Programming Model
Let:
- \( R \) = number of units of regular model
- \( C \) = number of units of catcher's model
Maximize:
\[ \text{Profit} = \text{(Enter coefficient for R)} R + \text{(Enter coefficient for C)} C \]
Subject to:
1. Cutting and Sewing Constraint:
\[ \text{(Enter coefficient for R)} R + \text{(Enter coefficient for C)} C \leq 700 \]
2. Finishing Constraint:
\[ \text{(Enter coefficient for R)} R + \text{(Enter coefficient for C)} C \leq 400 \]
3. Packaging and Shipping Constraint:
\[ \text{(Enter coefficient for R)} R + \text{(Enter coefficient for C)} C \leq 200 \]
4. Non-negativity Constraints:
\[ R, C \geq 0 \]
The model will help determine the optimal production quantities of regular and catcher’s models to maximize profit while staying within the department time constraints.
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