Given the profits and the quantities provided in the production possibility schedule, we need to determine which choice yields the largest profit.
First, we will calculate the total profit for each choice (A, B, and C):
For Choice A:
- Quantity of Donuts: 600
- Quantity of Bagels: 70
- Profit per Donut: \[tex]$0.50
- Profit per Bagel: \$[/tex]0.75
The total profit for Choice A is calculated as:
[tex]\[
\text{Profit (A)} = (600 \times 0.50) + (70 \times 0.75)
\][/tex]
[tex]\[
\text{Profit (A)} = 300 + 52.5 = 352.5
\][/tex]
Next, for Choice B:
- Quantity of Donuts: 500
- Quantity of Bagels: 140
- Profit per Donut: \[tex]$0.50
- Profit per Bagel: \$[/tex]0.75
The total profit for Choice B is calculated as:
[tex]\[
\text{Profit (B)} = (500 \times 0.50) + (140 \times 0.75)
\][/tex]
[tex]\[
\text{Profit (B)} = 250 + 105 = 355.0
\][/tex]
Finally, for Choice C:
- Quantity of Donuts: 500
- Quantity of Bagels: 40
- Profit per Donut: \[tex]$0.50
- Profit per Bagel: \$[/tex]0.75
The total profit for Choice C is calculated as:
[tex]\[
\text{Profit (C)} = (500 \times 0.50) + (40 \times 0.75)
\][/tex]
[tex]\[
\text{Profit (C)} = 250 + 30 = 280.0
\][/tex]
Now, we compare the total profits for Choices A, B, and C:
- Profit (A): 352.5
- Profit (B): 355.0
- Profit (C): 280.0
From these calculations, the largest profit is \$355.0, which corresponds to Choice B.
Therefore, Choice B yields the largest profit.
