Question
Which of the following production outcomes is not attainable for the given production possibilities curve?
A production possibilities curve is graphed with the horizontal axis labeled Tables from 0 to 25 in increments of 5 and the vertical axis labeled Benches from 0 to 35 in increments of 5. The first branch of the curve is a line segment that extends from left parenthesis 0 comma 30 right parenthesis to left parenthesis 4 comma 24 right parenthesis. The second branch of the curve is another line segment that extends from left parenthesis 4 comma 24 right parenthesis to left parenthesis 12 comma 20 right parenthesis. The last branch of the curve is a line segment that extends from left parenthesis 12 comma 20 right parenthesis to left parenthesis 20 comma 0 right parenthesis.
(1 point)
Responses
0 tables and 20 benches
0 tables and 20 benches
10 tables and 5 benches
10 tables and 5 benches
20 tables and 0 benches
20 tables and 0 benches
15 tables and 15 benches
A production possibilities curve is graphed with the horizontal axis labeled Tables from 0 to 25 in increments of 5 and the vertical axis labeled Benches from 0 to 35 in increments of 5. The first branch of the curve is a line segment that extends from left parenthesis 0 comma 30 right parenthesis to left parenthesis 4 comma 24 right parenthesis. The second branch of the curve is another line segment that extends from left parenthesis 4 comma 24 right parenthesis to left parenthesis 12 comma 20 right parenthesis. The last branch of the curve is a line segment that extends from left parenthesis 12 comma 20 right parenthesis to left parenthesis 20 comma 0 right parenthesis.
(1 point)
Responses
0 tables and 20 benches
0 tables and 20 benches
10 tables and 5 benches
10 tables and 5 benches
20 tables and 0 benches
20 tables and 0 benches
15 tables and 15 benches
Answers
GPT-4o mini
To determine which production outcome is not attainable given the production possibilities curve (PPC) described, we need to visualize or analyze the described points based on the segments defined:
1. **First Segment: From (0,30) to (4,24)** - This segment shows the trade-off between producing benches and tables. Here, if you produce 0 tables, you can produce up to 30 benches. If you produce 4 tables, you can produce 24 benches.
2. **Second Segment: From (4,24) to (12,20)** - In this range, for every increase in tables produced from 4 to 12, the number of benches decreases slightly from 24 to 20.
3. **Third Segment: From (12,20) to (20,0)** - As you produce more tables (from 12 to 20), you go down from 20 benches to none.
Now, let's analyze the specific outcomes given:
1. **0 tables and 20 benches** - This point is between (0,30) and (4,24) but is not on the curve. According to the first segment, if you produce only benches, you can produce 30 benches at 0 tables. Therefore, 20 benches is attainable.
2. **10 tables and 5 benches** - This point does not lie on the curve based on the connection between the segments provided.
3. **20 tables and 0 benches** - This point is at the endpoint of the curve, specifically (20,0) and is attainable.
4. **15 tables and 15 benches** - This point is not on the curve, as it falls within the production possibilities but is not feasible based on the segments described.
Based on this analysis, the production outcome that is not attainable within the limits defined by the production possibilities curve is **15 tables and 15 benches**. Therefore, that is the final answer.
1. **First Segment: From (0,30) to (4,24)** - This segment shows the trade-off between producing benches and tables. Here, if you produce 0 tables, you can produce up to 30 benches. If you produce 4 tables, you can produce 24 benches.
2. **Second Segment: From (4,24) to (12,20)** - In this range, for every increase in tables produced from 4 to 12, the number of benches decreases slightly from 24 to 20.
3. **Third Segment: From (12,20) to (20,0)** - As you produce more tables (from 12 to 20), you go down from 20 benches to none.
Now, let's analyze the specific outcomes given:
1. **0 tables and 20 benches** - This point is between (0,30) and (4,24) but is not on the curve. According to the first segment, if you produce only benches, you can produce 30 benches at 0 tables. Therefore, 20 benches is attainable.
2. **10 tables and 5 benches** - This point does not lie on the curve based on the connection between the segments provided.
3. **20 tables and 0 benches** - This point is at the endpoint of the curve, specifically (20,0) and is attainable.
4. **15 tables and 15 benches** - This point is not on the curve, as it falls within the production possibilities but is not feasible based on the segments described.
Based on this analysis, the production outcome that is not attainable within the limits defined by the production possibilities curve is **15 tables and 15 benches**. Therefore, that is the final answer.