To determine which scenario would represent a point on the production possibility frontier (PPF) for a country with 100 people, where it takes 10 people to produce 1 chair and 20 people to produce 1 desk, we need to analyze each given option:
### Option 1: 10 chairs and 10 desks
- People required for 10 chairs: [tex]\(10 \text{ chairs} \times 10 \text{ people per chair} = 100 \text{ people}\)[/tex]
- People required for 10 desks: [tex]\(10 \text{ desks} \times 20 \text{ people per desk} = 200 \text{ people}\)[/tex]
- Total people required: [tex]\(100 \text{ people} + 200 \text{ people} = 300 \text{ people}\)[/tex]
### Option 2: 5 chairs and 5 desks
- People required for 5 chairs: [tex]\(5 \text{ chairs} \times 10 \text{ people per chair} = 50 \text{ people}\)[/tex]
- People required for 5 desks: [tex]\(5 \text{ desks} \times 20 \text{ people per desk} = 100 \text{ people}\)[/tex]
- Total people required: [tex]\(50 \text{ people} + 100 \text{ people} = 150 \text{ people}\)[/tex]
### Option 3: 4 chairs and 7 desks
- People required for 4 chairs: [tex]\(4 \text{ chairs} \times 10 \text{ people per chair} = 40 \text{ people}\)[/tex]
- People required for 7 desks: [tex]\(7 \text{ desks} \times 20 \text{ people per desk} = 140 \text{ people}\)[/tex]
- Total people required: [tex]\(40 \text{ people} + 140 \text{ people} = 180 \text{ people}\)[/tex]
### Option 4: 4 chairs and 3 desks
- People required for 4 chairs: [tex]\(4 \text{ chairs} \times 10 \text{ people per chair} = 40 \text{ people}\)[/tex]
- People required for 3 desks: [tex]\(3 \text{ desks} \times 20 \text{ people per desk} = 60 \text{ people}\)[/tex]
- Total people required: [tex]\(40 \text{ people} + 60 \text{ people} = 100 \text{ people}\)[/tex]
Next, we compare the total people required for each option with the total available population (100 people):
1. 10 chairs and 10 desks: Requires 300 people (exceeds 100). Not on PPF.
2. 5 chairs and 5 desks: Requires 150 people (exceeds 100). Not on PPF.
3. 4 chairs and 7 desks: Requires 180 people (exceeds 100). Not on PPF.
4. 4 chairs and 3 desks: Requires 100 people (matches the 100 available). On PPF.
Conclusion: The combination of 4 chairs and 3 desks represents a point on the production possibility frontier (PPF).
