### Solving a Primitive Economy ProblemIn a primitive economy, the production of goods involves interdependent resources. Here, we will focus on two basic goods: yams and pork. #### Problem Statement:- **Yam Production:** Producing 1 bushel of yams requires 1/8 bushels of yams and 1/2 of a pig.- **Pig Production:** Producing 1 pig requires 1/3 bushel of yams.The task is to find the amount of each commodity (bushels of yams and number of pigs) that should be produced to achieve the target of 200 bushels of yams and 60 pigs.#### Requirements Calculation:- To produce 200 bushels of yams and 60 pigs, you need to calculate the required amounts of resources. To get 200 bushels of yams and 60 pigs requires bushels of yams and pigs. (Round to the nearest whole number as needed.)#### Explanation1. **Analyze the yam production**: Each bushel of yams requires 1/8 bushels of yams and 1/2 of a pig.2. **Analyze the pig production**: Each pig requires 1/3 bushel of yams.3. **Set up equations**: Use the given requirements to set up a system of linear equations or use a matrix solution approach.4. **Solve for the variables** to determine the exact amount of resources needed.This type of problem combines basic algebra with economic principles, illustrating how resource dependency in production can be mathematically mapped and resolved.### Further Learning:For further exploration, consider how changing the ratios or introducing additional goods would affect the economy's productivity and resource requirements.

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A primitive economy depends on two basic goods, yams and pork. Production of 1 bushel of yams requires 1/8 bushels of yams and 1/2 of a pig. To produce 1 pig requires 1/3 bushel of yams. Find the amount of each commodity that should be produced to get 200 bushels of yams and 60 pigs. pigs. To get 200 bushels of yams and 60 pigs requires bushels of yams and (Round to the nearest whole number as needed.)

A primitive economy depends on two basic goods, yams and pork. Production of 1 bushel of yams requires 1/8 bushels of yams and 1/2 of a pig. To produce 1 pig requires 1/3 bushel of yams. Find the amount of each commodity that should be produced to get 200 bushels of yams and 60 pigs. pigs. To get 200 bushels of yams and 60 pigs requires bushels of yams and (Round to the nearest whole number as needed.)

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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### Solving a Primitive Economy Problem

In a primitive economy, the production of goods involves interdependent resources. Here, we will focus on two basic goods: yams and pork.

#### Problem Statement:
- **Yam Production:** Producing 1 bushel of yams requires 1/8 bushels of yams and 1/2 of a pig.
- **Pig Production:** Producing 1 pig requires 1/3 bushel of yams.

The task is to find the amount of each commodity (bushels of yams and number of pigs) that should be produced to achieve the target of 200 bushels of yams and 60 pigs.

#### Requirements Calculation:
- To produce 200 bushels of yams and 60 pigs, you need to calculate the required amounts of resources.

<div style="margin-top: 1em; margin-bottom: 1em;">
<strong>To get 200 bushels of yams and 60 pigs requires</strong>
<input type="text" id="yams-required" placeholder="___"> bushels of yams and
<input type="text" id="pigs-required" placeholder="___"> pigs.
(Round to the nearest whole number as needed.)
</div>

#### Explanation
1. **Analyze the yam production**: Each bushel of yams requires 1/8 bushels of yams and 1/2 of a pig.
2. **Analyze the pig production**: Each pig requires 1/3 bushel of yams.
3. **Set up equations**: Use the given requirements to set up a system of linear equations or use a matrix solution approach.
4. **Solve for the variables** to determine the exact amount of resources needed.

This type of problem combines basic algebra with economic principles, illustrating how resource dependency in production can be mathematically mapped and resolved.

### Further Learning:
For further exploration, consider how changing the ratios or introducing additional goods would affect the economy's productivity and resource requirements.

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