To determine which choice yields the largest profit for the pastry shop, we need to evaluate the profit from each option based on the given quantities and profits per item. We are provided with the following details:
- Profit per donut: [tex]\(\$0.50\)[/tex]
- Profit per bagel: [tex]\(\$0.75\)[/tex]
The production possibilities are as follows:
| Choice | Quantity of Donuts | Quantity of Bagels |
|--------|--------------------|--------------------|
| A | 600 | 70 |
| B | 500 | 140 |
| C | 500 | 40 |
We will calculate the total profit for each choice:
### Choice A
- Number of donuts: 600
- Number of bagels: 70
Calculation for Choice A:
[tex]\[
\text{Profit from donuts} = 600 \text{ donuts} \times 0.50 \text{ dollars per donut} = 300 \text{ dollars}
\][/tex]
[tex]\[
\text{Profit from bagels} = 70 \text{ bagels} \times 0.75 \text{ dollars per bagel} = 52.5 \text{ dollars}
\][/tex]
[tex]\[
\text{Total profit for Choice A} = 300 \text{ dollars} + 52.5 \text{ dollars} = 352.5 \text{ dollars}
\][/tex]
### Choice B
- Number of donuts: 500
- Number of bagels: 140
Calculation for Choice B:
[tex]\[
\text{Profit from donuts} = 500 \text{ donuts} \times 0.50 \text{ dollars per donut} = 250 \text{ dollars}
\][/tex]
[tex]\[
\text{Profit from bagels} = 140 \text{ bagels} \times 0.75 \text{ dollars per bagel} = 105 \text{ dollars}
\][/tex]
[tex]\[
\text{Total profit for Choice B} = 250 \text{ dollars} + 105 \text{ dollars} = 355 \text{ dollars}
\][/tex]
### Choice C
- Number of donuts: 500
- Number of bagels: 40
Calculation for Choice C:
[tex]\[
\text{Profit from donuts} = 500 \text{ donuts} \times 0.50 \text{ dollars per donut} = 250 \text{ dollars}
\][/tex]
[tex]\[
\text{Profit from bagels} = 40 \text{ bagels} \times 0.75 \text{ dollars per bagel} = 30 \text{ dollars}
\][/tex]
[tex]\[
\text{Total profit for Choice C} = 250 \text{ dollars} + 30 \text{ dollars} = 280 \text{ dollars}
\][/tex]
### Comparison of Profits
- Profit for Choice A: 352.5 dollars
- Profit for Choice B: 355 dollars
- Profit for Choice C: 280 dollars
From the above calculations, we can see that Choice B yields the highest profit of 355 dollars.
Therefore, Choice B is the one that yields the largest profit.
