Juan Pablo runs a factory that makes Blu-ray players. Each T50 takes 6 ounces of plastic and 4 ounces of metal. Each G150 requires 3 ounces of plastic and 8 ounces of metal. The factory has 282 ounces of plastic, 560 ounces of metal available, with a maximum of 22 T50 that can be built each week. If each T50 generates $19 in profit, and each G150 generates $15, how many of each of the Blu-ray players should Juan Pablo have the factory make each week to make the most profit? T50: G150: Best profit:
Juan Pablo runs a factory that makes Blu-ray players. Each T50 takes 6 ounces of plastic and 4 ounces of metal. Each G150 requires 3 ounces of plastic and 8 ounces of metal. The factory has 282 ounces of plastic, 560 ounces of metal available, with a maximum of 22 T50 that can be built each week. If each T50 generates $19 in profit, and each G150 generates $15, how many of each of the Blu-ray players should Juan Pablo have the factory make each week to make the most profit? T50: 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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Transcribed Image Text:### Maximizing Profit for Blu-ray Player Production
Juan Pablo runs a factory that manufactures Blu-ray players. The factory produces two different models: T50 and G150. Here is the breakdown of the materials and profit for each model:
- **T50 model:**
- Requires:
- 6 ounces of plastic
- 4 ounces of metal
- Generates:
- $19 in profit per unit
- **G150 model:**
- Requires:
- 3 ounces of plastic
- 8 ounces of metal
- Generates:
- $15 in profit per unit
The factory's resources are limited to:
- 282 ounces of plastic
- 560 ounces of metal
- A maximum production capacity of 22 units of T50 each week
### Problem Statement
To maximize profit, the factory needs to determine how many of each Blu-ray player model (T50 and G150) should be produced each week within the given constraints.
- **Constraints:**
- Plastic usage: `6x + 3y ≤ 282`
- Metal usage: `4x + 8y ≤ 560`
- Production limit for T50: `x ≤ 22`
Here, `x` is the number of T50 units, and `y` is the number of G150 units.
### Maximize Profit
The objective is to maximize the profit function:
- Total Profit = `19x + 15y`
Please determine the number of each model that should be produced weekly for maximum profit and record your findings in the fields below.
- **G150**:
- **T50**:
- **Best Profit**:
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