A company manufactures x units of Product A and y units of Product B, on two machines, I and II. It has been determined that the company will realize a profit of $2/unit of Product A and a profit of $4/unit of Product B. To manufacture a unit of Product A requires 6 min on Machine I and 5 min on Machine II. To manufacture a unit of Product B requires 9 min on Machine I and 4 min on Machine II. There are 5 hr of machine time available on Machine I and 3 hr of machine time available on Machine II in each work shift. How many units of each product should be produced in each shift to maximize the company's profit? (x, y) = What is the optimal profit? (Round your answer to the nearest whole number.)
A company manufactures x units of Product A and y units of Product B, on two machines, I and II. It has been determined that the company will realize a profit of $2/unit of Product A and a profit of $4/unit of Product B. To manufacture a unit of Product A requires 6 min on Machine I and 5 min on Machine II. To manufacture a unit of Product B requires 9 min on Machine I and 4 min on Machine II. There are 5 hr of machine time available on Machine I and 3 hr of machine time available on Machine II in each work shift. How many units of each product should be produced in each shift to maximize the company's profit? (x, y) = What is the optimal profit? (Round your answer to the nearest whole number.)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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![### Optimization Problem in Manufacturing
A company manufactures \( x \) units of Product A and \( y \) units of Product B, on two machines, I and II. It has been determined that the company will realize a profit of **$2**/unit of Product A and a profit of **$4**/unit of Product B. To manufacture a unit of Product A requires 6 minutes on Machine I and 5 minutes on Machine II. To manufacture a unit of Product B requires 9 minutes on Machine I and 4 minutes on Machine II. There are 5 hours of machine time available on Machine I and 3 hours of machine time available on Machine II in each work shift.
#### Problem:
How many units of each product should be produced in each shift to maximize the company's profit?
#### Solution Representation:
The solution is represented as:
\[ (x, y) = \left( \_\_\_\_ \right) \]
Please fill in the number of units of Product A (\( x \)) and Product B (\( y \)) in the blank provided.
#### Optimal Profit Calculation:
What is the optimal profit? (Round your answer to the nearest whole number.)
\[ \$ \_\_\_\_ \]
To solve this problem, you need to set up and solve a linear programming problem using the given constraints and profit information.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4e80d594-14a8-4713-8ea5-1fda205a6b86%2Fd8d8b672-e4e9-489e-b1cc-c21cd71b2600%2Fn434006.png&w=3840&q=75)
Transcribed Image Text:### Optimization Problem in Manufacturing
A company manufactures \( x \) units of Product A and \( y \) units of Product B, on two machines, I and II. It has been determined that the company will realize a profit of **$2**/unit of Product A and a profit of **$4**/unit of Product B. To manufacture a unit of Product A requires 6 minutes on Machine I and 5 minutes on Machine II. To manufacture a unit of Product B requires 9 minutes on Machine I and 4 minutes on Machine II. There are 5 hours of machine time available on Machine I and 3 hours of machine time available on Machine II in each work shift.
#### Problem:
How many units of each product should be produced in each shift to maximize the company's profit?
#### Solution Representation:
The solution is represented as:
\[ (x, y) = \left( \_\_\_\_ \right) \]
Please fill in the number of units of Product A (\( x \)) and Product B (\( y \)) in the blank provided.
#### Optimal Profit Calculation:
What is the optimal profit? (Round your answer to the nearest whole number.)
\[ \$ \_\_\_\_ \]
To solve this problem, you need to set up and solve a linear programming problem using the given constraints and profit information.
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