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.)

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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.
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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