### 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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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:

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:

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.

Topic Video

Question

### 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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