Devin runs a factory that makes Blu-ray players. Each R80 takes 9 ounces of plastic and 2 ounces of metal. Each G150 requires 3 ounces of plastic and 6 ounces of metal. The factory has 270 ounces of plastic, 348 ounces of metal available, with a maximum of 18 R80 that can be built each week. If each R80 generates $8 in profit, and each G150 generates $9, how many of each of the Blu-ray players should Devin have the factory make each week to make the most profit? R80: G150: Best profit:

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### Maximizing Profit in Blu-ray Player Production - A Case Study

**Problem Statement:**

Devin runs a factory that manufactures Blu-ray players. The factory produces two models: R80 and G150. 

- **R80 Specifications:**
  - Requires 9 ounces of plastic and 2 ounces of metal.
  - Generates $8 in profit.
  - Maximum production limit: 18 units per week.

- **G150 Specifications:**
  - Requires 3 ounces of plastic and 6 ounces of metal.
  - Generates $9 in profit.

**Resource Constraints:**

The factory has:
- 270 ounces of plastic available each week.
- 348 ounces of metal available each week.

**Objective:**

Determine the optimal number of each Blu-ray player model (R80 and G150) to produce each week to achieve the maximum profit.

**Question:**

How many units of R80 and G150 should Devin's factory produce each week to maximize profit?

**Solution:**

To find the solution, the following details need to be considered:

- The total amount of resources (plastic and metal) used should not exceed the available resources.
- The production should potentially include a mix of both R80 and G150 that maximizes the profit.

The form provided below is used to record the optimal production quantities and the corresponding maximum profit:

- **R80:**
  - (Optimal number of R80 units)

- **G150:**
  - (Optimal number of G150 units)

- **Best Profit:**
  - (Maximized Profit in dollars)

By calculating the optimal production quantities based on the given constraints and profit generation, the factory can ensure the most efficient use of resources and maximize their earnings.

**Graphical Representation:**

The problem can often be visualized graphically by plotting the resource constraints on a graph and finding the feasible region. The vertices of this region can be examined to determine the combination of R80 and G150 units that results in the highest profit. However, for educational purposes, this would typically involve creating a linear programming model and solving it using methods such as the Simplex algorithm.
Transcribed Image Text:### Maximizing Profit in Blu-ray Player Production - A Case Study **Problem Statement:** Devin runs a factory that manufactures Blu-ray players. The factory produces two models: R80 and G150. - **R80 Specifications:** - Requires 9 ounces of plastic and 2 ounces of metal. - Generates $8 in profit. - Maximum production limit: 18 units per week. - **G150 Specifications:** - Requires 3 ounces of plastic and 6 ounces of metal. - Generates $9 in profit. **Resource Constraints:** The factory has: - 270 ounces of plastic available each week. - 348 ounces of metal available each week. **Objective:** Determine the optimal number of each Blu-ray player model (R80 and G150) to produce each week to achieve the maximum profit. **Question:** How many units of R80 and G150 should Devin's factory produce each week to maximize profit? **Solution:** To find the solution, the following details need to be considered: - The total amount of resources (plastic and metal) used should not exceed the available resources. - The production should potentially include a mix of both R80 and G150 that maximizes the profit. The form provided below is used to record the optimal production quantities and the corresponding maximum profit: - **R80:** - (Optimal number of R80 units) - **G150:** - (Optimal number of G150 units) - **Best Profit:** - (Maximized Profit in dollars) By calculating the optimal production quantities based on the given constraints and profit generation, the factory can ensure the most efficient use of resources and maximize their earnings. **Graphical Representation:** The problem can often be visualized graphically by plotting the resource constraints on a graph and finding the feasible region. The vertices of this region can be examined to determine the combination of R80 and G150 units that results in the highest profit. However, for educational purposes, this would typically involve creating a linear programming model and solving it using methods such as the Simplex algorithm.
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