To analyze the trends in the marginal cost of producing apple pies, let's break down the observations step by step.
1. Initial changes in marginal cost:
- For the first few pies produced, observe how the marginal cost changes.
- From 0 pies to 1 pie, the marginal cost is [tex]\(\$1.00\)[/tex].
- From 1 pie to 2 pies, the marginal cost decreases to [tex]\(\$0.50\)[/tex].
- From 2 pies to 3 pies, the marginal cost further decreases to [tex]\(\$0.25\)[/tex].
As we can see, the marginal cost decreases from 1.00 to 0.50 to 0.25. Thus, [tex]\(M1 > M2 > M3\)[/tex], so the marginal cost initially decreases as production increases.
2. Further changes in marginal cost:
- From 3 pies to 4 pies, the marginal cost increases to [tex]\(\$0.50\)[/tex].
- From 4 pies to 5 pies, the marginal cost further increases to [tex]\(\$1.25\)[/tex].
- From 5 pies to 6 pies, the marginal cost slightly increases to [tex]\(\$1.50\)[/tex].
Here, the trend reverses, and we see the marginal cost starting to increase after the initial decrease.
3. Eventual patterns:
- Consider the last three values of marginal costs to identify any eventual decrease/increase trend.
- The values went from [tex]\(\$0.50\)[/tex] to [tex]\(\$1.25\)[/tex] to [tex]\(\$1.50\)[/tex] for pies produced from 4 to 6 respectively.
These values show that as production continues, the marginal cost increases and does not show further decrease within this range.
Thus, based on the observed patterns from the tabulated data:
- Initial Trend: The marginal cost initially decreases as production (number of pies) increases.
- Initial Increase: There is no significant initial increase observed directly from the start; it rather decreases initially.
- Eventual Decrease: The cost does not eventually decrease as production increases because it continues to increase towards the end.
Therefore, the comprehensive analysis of the marginal cost trends aligns with the answer:
- Initially decreases as production increases: True
- Initially increases as production increases: False
- Eventually decreases as production increases: False
This matches the result of (False, True, True) extracted from the analysis.
