e) Solve the mixed-integer linear program formulated in part (d). How much of each product should be produced and what is the projected total profit contribution? Compare this profit contribution to that obtained in part (c). If required, round your answers to nearest whole number. If your answer is zero enter "0". Product 1 Product 2 Product 3 00 Amount to Produce Updated Profit
e) Solve the mixed-integer linear program formulated in part (d). How much of each product should be produced and what is the projected total profit contribution? Compare this profit contribution to that obtained in part (c). If required, round your answers to nearest whole number. If your answer is zero enter "0". Product 1 Product 2 Product 3 00 Amount to Produce Updated Profit
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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Please help in solving Part (e)
![**Hart Manufacturing Product Optimization**
Hart Manufacturing produces three products, each requiring specific operations in three departments: A, B, and C. Below are details for labor-hour requirements per department and profit contributions per product.
**Department Labor-Hour Requirements (per unit):**
| Department | Product 1 | Product 2 | Product 3 |
|------------|-----------|-----------|-----------|
| A | 1.50 | 3.00 | 2.50 |
| B | 2.00 | 1.50 | 2.00 |
| C | 0.25 | 0.25 | 0.25 |
During the next production period, available labor-hours are: 450 in Department A, 350 in Department B, and 50 in Department C. The profit contributions are: $25 per unit for Product 1, $28 for Product 2, and $30 for Product 3.
**(a) Linear Programming Model for Profit Maximization**
Objective: Maximize profit \( Z = 25P_1 + 28P_2 + 30P_3 \)
Subject to:
\[
\begin{align*}
1.5P_1 + 3P_2 + 2.5P_3 & \leq 450 \quad \text{(Dept A constraint)} \\
2P_1 + 1.5P_2 + 2P_3 & \leq 350 \quad \text{(Dept B constraint)} \\
0.25P_1 + 0.25P_2 + 0.25P_3 & \leq 50 \quad \text{(Dept C constraint)} \\
P_1, P_2, P_3 & \geq 0 \quad \text{and integer}
\end{align*}
\]
**(b) Solution to Linear Program**
Production recommendation:
| Product | Amount to Produce |
|-------------|-------------------|
| Product 1 | 60 |
| Product 2 | 80 |
| Product 3 | 60 |
Total Profit: \$5540
**(c) Production Setup Costs**
Setup costs: $550 for Product 1, $400 for Product 2, $600 for Product 3.
Revised Total Profit after setup](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb894e8fe-1c5c-40b2-9b0c-b397d4783847%2F5585ad18-45cb-45da-92ad-8b2c6c72d17b%2F1w9cwi_processed.png&w=3840&q=75)
Transcribed Image Text:**Hart Manufacturing Product Optimization**
Hart Manufacturing produces three products, each requiring specific operations in three departments: A, B, and C. Below are details for labor-hour requirements per department and profit contributions per product.
**Department Labor-Hour Requirements (per unit):**
| Department | Product 1 | Product 2 | Product 3 |
|------------|-----------|-----------|-----------|
| A | 1.50 | 3.00 | 2.50 |
| B | 2.00 | 1.50 | 2.00 |
| C | 0.25 | 0.25 | 0.25 |
During the next production period, available labor-hours are: 450 in Department A, 350 in Department B, and 50 in Department C. The profit contributions are: $25 per unit for Product 1, $28 for Product 2, and $30 for Product 3.
**(a) Linear Programming Model for Profit Maximization**
Objective: Maximize profit \( Z = 25P_1 + 28P_2 + 30P_3 \)
Subject to:
\[
\begin{align*}
1.5P_1 + 3P_2 + 2.5P_3 & \leq 450 \quad \text{(Dept A constraint)} \\
2P_1 + 1.5P_2 + 2P_3 & \leq 350 \quad \text{(Dept B constraint)} \\
0.25P_1 + 0.25P_2 + 0.25P_3 & \leq 50 \quad \text{(Dept C constraint)} \\
P_1, P_2, P_3 & \geq 0 \quad \text{and integer}
\end{align*}
\]
**(b) Solution to Linear Program**
Production recommendation:
| Product | Amount to Produce |
|-------------|-------------------|
| Product 1 | 60 |
| Product 2 | 80 |
| Product 3 | 60 |
Total Profit: \$5540
**(c) Production Setup Costs**
Setup costs: $550 for Product 1, $400 for Product 2, $600 for Product 3.
Revised Total Profit after setup
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