**Problem Statement:**An electronics company produces transistors, resistors, and computer chips. The production of each item requires specific amounts of copper, zinc, and glass:- **Transistor requirements:** - 3 units of copper - 2 units of zinc - 1 unit of glass- **Resistor requirements:** - 3 units of copper - 1 unit of zinc - 2 units of glass- **Computer chip requirements:** - 2 units of copper - 1 unit of zinc - 2 units of glass**Available resources:**- 2860 units of copper- 1375 units of zinc- 1745 units of glass**Task:**Determine how many transistors, resistors, and computer chips can be produced using the available resources by solving this problem with the inverse of the coefficient matrix to solve a system of equations.**Solution:**Set up a system of equations based on the requirements:Let $ x $ be the number of transistors, $ y $ be the number of resistors, and $ z $ be the number of computer chips.The system of equations is:1. $ 3x + 3y + 2z = 2860 $2. $ 2x + 1y + 1z = 1375 $3. $ 1x + 2y + 2z = 1745 $Use the inverse of the coefficient matrix of this system to find the values of $ x $, $ y $, and $ z $. Once solved, fill in the blanks with the number of transistors, resistors, and computer chips the company can manufacture.

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Description: **Problem Statement:**An electronics company produces transistors, resistors, and computer chips. The production of each item requires specific amounts of copper, zinc, and glass:- **Transistor requirements:** - 3 units of copper - 2 units of zin

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An electronics company produces transistors, resistors, and computer chips. Each transistor requires 3 units of copper, 2 units of zinc, and 1 unit of glass. Each resistor requires 3, 1, and 2 units of the three materials, and each computer chip requires 2, 1, and 2 units of these materials, respectively. How many of each product can be made with 2860 units of copper, 1375 units of zinc, and 1745 units of glass? Solve this exercise by using the inverse of the coefficient matrix to solve a system of equations. The company can make transistors, resistors, and computer chips.

An electronics company produces transistors, resistors, and computer chips. Each transistor requires 3 units of copper, 2 units of zinc, and 1 unit of glass. Each resistor requires 3, 1, and 2 units of the three materials, and each computer chip requires 2, 1, and 2 units of these materials, respectively. How many of each product can be made with 2860 units of copper, 1375 units of zinc, and 1745 units of glass? Solve this exercise by using the inverse of the coefficient matrix to solve a system of equations. The company can make transistors, resistors, and computer chips.

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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**Problem Statement:**

An electronics company produces transistors, resistors, and computer chips. The production of each item requires specific amounts of copper, zinc, and glass:

- **Transistor requirements:**
- 3 units of copper
- 2 units of zinc
- 1 unit of glass

- **Resistor requirements:**
- 3 units of copper
- 1 unit of zinc
- 2 units of glass

- **Computer chip requirements:**
- 2 units of copper
- 1 unit of zinc
- 2 units of glass

**Available resources:**
- 2860 units of copper
- 1375 units of zinc
- 1745 units of glass

**Task:**
Determine how many transistors, resistors, and computer chips can be produced using the available resources by solving this problem with the inverse of the coefficient matrix to solve a system of equations.

**Solution:**
Set up a system of equations based on the requirements:

Let $ x $ be the number of transistors, $ y $ be the number of resistors, and $ z $ be the number of computer chips.

The system of equations is:
1. $ 3x + 3y + 2z = 2860 $
2. $ 2x + 1y + 1z = 1375 $
3. $ 1x + 2y + 2z = 1745 $

Use the inverse of the coefficient matrix of this system to find the values of $ x $, $ y $, and $ z $. Once solved, fill in the blanks with the number of transistors, resistors, and computer chips the company can manufacture.

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An electronics company produces transistors, resistors, and computer chips. Each transistor requires 3 units of copper, 1 unit of zinc, and 2 units of glass. Each resistor requires 3 units of copper, 2 units of zinc, and 1 unit of glass. Each computer chip requires 2 units of copper, 1 unit of zinc, and 2 units of glass. The company has a total of 810 units of copper, 450 units of zinc, and 480 units of glass available for production. Assuming that all of the copper, zinc, and glass is used in production, how many resistors will be produced?