To determine what will most likely happen if the pie maker bakes a seventh pie, let's analyze the given data carefully and predict the trends in marginal costs and marginal revenues.
Here, we have the following information:
[tex]\[
\begin{array}{|c|c|c|c|c|c|}
\hline
\text{Pies produced per day} & \text{Total cost} & \text{Marginal cost} & \text{Total revenue} & \text{Marginal revenue} & \text{Profit} \\
\hline
0 & \[tex]$0.00 & \$[/tex]0.00 & - & - & \$0.00 \\
\hline
1 & \[tex]$1.00 & \$[/tex]1.00 & \[tex]$10.00 & \$[/tex]10.00 & \$9.00 \\
\hline
2 & \[tex]$1.50 & \$[/tex]0.50 & \[tex]$20.00 & \$[/tex]10.00 & \$18.50 \\
\hline
3 & \[tex]$1.75 & \$[/tex]0.25 & \[tex]$30.00 & \$[/tex]10.00 & \$28.25 \\
\hline
4 & \[tex]$2.25 & \$[/tex]0.50 & \[tex]$40.00 & \$[/tex]10.00 & \$37.75 \\
\hline
5 & \[tex]$3.50 & \$[/tex]1.25 & \[tex]$50.00 & \$[/tex]10.00 & \$46.50 \\
\hline
6 & \[tex]$5.00 & \$[/tex]1.50 & \[tex]$60.00 & \$[/tex]10.00 & \$55.00 \\
\hline
\end{array}
\][/tex]
### Step-by-Step Analysis:
1. Marginal Cost Trend:
- The marginal cost has been:
- \$1.00 for the 1st pie.
- \$0.50 for the 2nd pie.
- \$0.25 for the 3rd pie.
- \$0.50 for the 4th pie.
- \$1.25 for the 5th pie.
- \$1.50 for the 6th pie.
- Observing the trend, the marginal cost does not follow a simple linear trend (it's not consistently increasing or decreasing). But looking particularly at the transition from the 5th pie to the 6th pie, there is an increase from \[tex]$1.25 to \$[/tex]1.50.
2. Prediction for Marginal Cost:
- Given the recent increase trend from \[tex]$1.25 to \$[/tex]1.50, it is more reasonable to expect that the marginal cost might continue to increase slightly for the 7th pie. Therefore, it's likely to increase to around \$2.00 for the next pie.
3. Marginal Revenue Trend:
- The marginal revenue has remained constant at \$10.00 for all the pies produced (from 1st to 6th).
- There are no indications in the data to suggest a change in this trend.
4. Prediction for Marginal Revenue:
- Considering the consistency of the marginal revenue at \$10.00, it is reasonable to predict that the marginal revenue will stay the same for the 7th pie production.
### Conclusion:
- Marginal Cost:
The marginal cost will most likely increase to \$2.00.
- Marginal Revenue:
The marginal revenue will most likely stay the same at \$10.00.
Thus, based on the given data trends, the correct conclusion is:
The marginal cost will most likely increase to \$2.00.
