To determine which option yields the highest profit, we need to calculate the total profit for each choice. We know that the profit per donut is \[tex]$0.50 and the profit per bagel is \$[/tex]0.75. Let's break down the calculations for Choices A, B, and C:
1. Choice A:
- Quantity of Donuts: 600
- Quantity of Bagels: 70
- Profit per Donut: \[tex]$0.50
- Profit per Bagel: \$[/tex]0.75
Total Profit for Choice A:
[tex]\[
\text{Profit}_A = (600 \text{ donuts} \times \$0.50/\text{donut}) + (70 \text{ bagels} \times \$0.75/\text{bagel})
\][/tex]
[tex]\[
\text{Profit}_A = (600 \times 0.50) + (70 \times 0.75)
\][/tex]
[tex]\[
\text{Profit}_A = 300 + 52.5 = 352.5 \text{ dollars}
\][/tex]
2. Choice B:
- Quantity of Donuts: 500
- Quantity of Bagels: 140
- Profit per Donut: \[tex]$0.50
- Profit per Bagel: \$[/tex]0.75
Total Profit for Choice B:
[tex]\[
\text{Profit}_B = (500 \text{ donuts} \times \$0.50/\text{donut}) + (140 \text{ bagels} \times \$0.75/\text{bagel})
\][/tex]
[tex]\[
\text{Profit}_B = (500 \times 0.50) + (140 \times 0.75)
\][/tex]
[tex]\[
\text{Profit}_B = 250 + 105 = 355 \text{ dollars}
\][/tex]
3. Choice C:
- Quantity of Donuts: 500
- Quantity of Bagels: 40
- Profit per Donut: \[tex]$0.50
- Profit per Bagel: \$[/tex]0.75
Total Profit for Choice C:
[tex]\[
\text{Profit}_C = (500 \text{ donuts} \times \$0.50/\text{donut}) + (40 \text{ bagels} \times \$0.75/\text{bagel})
\][/tex]
[tex]\[
\text{Profit}_C = (500 \times 0.50) + (40 \times 0.75)
\][/tex]
[tex]\[
\text{Profit}_C = 250 + 30 = 280 \text{ dollars}
\][/tex]
After calculating the total profits for each choice, we can see the following results:
- Profit for Choice A: \[tex]$352.5
- Profit for Choice B: \$[/tex]355.0
- Profit for Choice C: \[tex]$280.0
Thus, the option yielding the largest profit is Choice B with a total profit of \$[/tex]355.0.
