Answer :
To determine which choice yields the largest profit, we need to calculate the profit for each choice based on the given quantities of donuts and bagels and their respective profits. Let's go through each choice step-by-step:
Profit Calculation Details:
1. Choice A:
- Quantity of Donuts: 600
- Quantity of Bagels: 70
- Profit per Donut: \[tex]$0.50 - Profit per Bagel: \$[/tex]0.75
Calculate the total profit for Choice A:
[tex]\[ \text{Total Profit for A} = (\text{Quantity of Donuts} \times \text{Profit per Donut}) + (\text{Quantity of Bagels} \times \text{Profit per Bagel}) \][/tex]
[tex]\[ \text{Total Profit for A} = (600 \times 0.50) + (70 \times 0.75) \][/tex]
[tex]\[ \text{Total Profit for A} = 300 + 52.5 = 352.5 \][/tex]
2. Choice B:
- Quantity of Donuts: 500
- Quantity of Bagels: 140
- Profit per Donut: \[tex]$0.50 - Profit per Bagel: \$[/tex]0.75
Calculate the total profit for Choice B:
[tex]\[ \text{Total Profit for B} = (\text{Quantity of Donuts} \times \text{Profit per Donut}) + (\text{Quantity of Bagels} \times \text{Profit per Bagel}) \][/tex]
[tex]\[ \text{Total Profit for B} = (500 \times 0.50) + (140 \times 0.75) \][/tex]
[tex]\[ \text{Total Profit for B} = 250 + 105 = 355 \][/tex]
3. Choice C:
- Quantity of Donuts: 500
- Quantity of Bagels: 0
- Profit per Donut: \[tex]$0.50 - Profit per Bagel: \$[/tex]0.75
Calculate the total profit for Choice C:
[tex]\[ \text{Total Profit for C} = (\text{Quantity of Donuts} \times \text{Profit per Donut}) + (\text{Quantity of Bagels} \times \text{Profit per Bagel}) \][/tex]
[tex]\[ \text{Total Profit for C} = (500 \times 0.50) + (0 \times 0.75) \][/tex]
[tex]\[ \text{Total Profit for C} = 250 + 0 = 250 \][/tex]
Determine the Choice with the Largest Profit:
- Total Profit for Choice A: \[tex]$352.5 - Total Profit for Choice B: \$[/tex]355.0
- Total Profit for Choice C: \[tex]$250.0 Comparing these profits, we see that Choice B yields the largest profit, which is \$[/tex]355.0. Therefore, Choice B yields the largest profit.
Profit Calculation Details:
1. Choice A:
- Quantity of Donuts: 600
- Quantity of Bagels: 70
- Profit per Donut: \[tex]$0.50 - Profit per Bagel: \$[/tex]0.75
Calculate the total profit for Choice A:
[tex]\[ \text{Total Profit for A} = (\text{Quantity of Donuts} \times \text{Profit per Donut}) + (\text{Quantity of Bagels} \times \text{Profit per Bagel}) \][/tex]
[tex]\[ \text{Total Profit for A} = (600 \times 0.50) + (70 \times 0.75) \][/tex]
[tex]\[ \text{Total Profit for A} = 300 + 52.5 = 352.5 \][/tex]
2. Choice B:
- Quantity of Donuts: 500
- Quantity of Bagels: 140
- Profit per Donut: \[tex]$0.50 - Profit per Bagel: \$[/tex]0.75
Calculate the total profit for Choice B:
[tex]\[ \text{Total Profit for B} = (\text{Quantity of Donuts} \times \text{Profit per Donut}) + (\text{Quantity of Bagels} \times \text{Profit per Bagel}) \][/tex]
[tex]\[ \text{Total Profit for B} = (500 \times 0.50) + (140 \times 0.75) \][/tex]
[tex]\[ \text{Total Profit for B} = 250 + 105 = 355 \][/tex]
3. Choice C:
- Quantity of Donuts: 500
- Quantity of Bagels: 0
- Profit per Donut: \[tex]$0.50 - Profit per Bagel: \$[/tex]0.75
Calculate the total profit for Choice C:
[tex]\[ \text{Total Profit for C} = (\text{Quantity of Donuts} \times \text{Profit per Donut}) + (\text{Quantity of Bagels} \times \text{Profit per Bagel}) \][/tex]
[tex]\[ \text{Total Profit for C} = (500 \times 0.50) + (0 \times 0.75) \][/tex]
[tex]\[ \text{Total Profit for C} = 250 + 0 = 250 \][/tex]
Determine the Choice with the Largest Profit:
- Total Profit for Choice A: \[tex]$352.5 - Total Profit for Choice B: \$[/tex]355.0
- Total Profit for Choice C: \[tex]$250.0 Comparing these profits, we see that Choice B yields the largest profit, which is \$[/tex]355.0. Therefore, Choice B yields the largest profit.
