The chart below shows a production possibility schedule for a pastry shop that makes [tex]$0.50 profit per donut and $[/tex]0.75 profit per bagel.

\begin{tabular}{|l|l|l|}
\hline
Choice & \begin{tabular}{l}
Quantity of \\
Donuts
\end{tabular} & \begin{tabular}{l}
Quantity of \\
Bagels
\end{tabular} \\
\hline
A & 600 & 70 \\
\hline
B & 500 & 140 \\
\hline
C & 500 & 40 \\
\hline
\end{tabular}

Which choice yields the largest profit?

A. Choice A
B. Choice B
C. Choice C



Answer :

To determine which choice yields the largest profit, we need to calculate the total profit for each choice using the given profit per donut and per bagel.

1. Profit per Donut: [tex]\( \$0.30 \)[/tex]
2. Profit per Bagel: [tex]\( \$0.75 \)[/tex]

We'll use these profit values to compute the total profit for each choice (A, B, and C).

### Choice A:
- Quantity of Donuts: 600
- Quantity of Bagels: 70

Total Profit for Choice A:
[tex]\[ \text{Profit from Donuts} = 600 \times 0.30 = 180.00 \][/tex]
[tex]\[ \text{Profit from Bagels} = 70 \times 0.75 = 52.50 \][/tex]
[tex]\[ \text{Total Profit for Choice A} = 180.00 + 52.50 = 232.50 \][/tex]

### Choice B:
- Quantity of Donuts: 500
- Quantity of Bagels: 140

Total Profit for Choice B:
[tex]\[ \text{Profit from Donuts} = 500 \times 0.30 = 150.00 \][/tex]
[tex]\[ \text{Profit from Bagels} = 140 \times 0.75 = 105.00 \][/tex]
[tex]\[ \text{Total Profit for Choice B} = 150.00 + 105.00 = 255.00 \][/tex]

### Choice C:
- Quantity of Donuts: 500
- Quantity of Bagels: 40

Total Profit for Choice C:
[tex]\[ \text{Profit from Donuts} = 500 \times 0.30 = 150.00 \][/tex]
[tex]\[ \text{Profit from Bagels} = 40 \times 0.75 = 30.00 \][/tex]
[tex]\[ \text{Total Profit for Choice C} = 150.00 + 30.00 = 180.00 \][/tex]

### Comparison of the Total Profits:
- Total Profit for Choice A: [tex]$232.50 - Total Profit for Choice B: $[/tex]255.00
- Total Profit for Choice C: [tex]$180.00 Among these, the choice that yields the largest profit is Choice B with a total profit of $[/tex]255.00.

Thus, Choice [tex]$\boxed{B}$[/tex] yields the largest profit.