To determine which choice yields the largest profit for the pastry shop, we will calculate the total profit for each choice and compare them.
### Given Data:
- Profit per donut: \[tex]$0.50
- Profit per bagel: \$[/tex]0.75
### Choices:
| Choice | Quantity of Donuts | Quantity of Bagels |
|--------|---------------------|--------------------|
| A | 600 | 70 |
| B | 500 | 140 |
| C | 500 | 40 |
We need to calculate the profit for each choice by using the formula for total profit:
[tex]\[ \text{Total Profit} = (\text{Quantity of Donuts} \times \text{Profit per Donut}) + (\text{Quantity of Bagels} \times \text{Profit per Bagel}) \][/tex]
### Step-by-Step Calculation:
#### Choice A:
- Quantity of Donuts: 600
- Quantity of Bagels: 70
- Profit from Donuts: [tex]\( 600 \times 0.50 = 300 \)[/tex]
- Profit from Bagels: [tex]\( 70 \times 0.75 = 52.5 \)[/tex]
- Total Profit for Choice A: [tex]\( 300 + 52.5 = 352.5 \)[/tex]
#### Choice B:
- Quantity of Donuts: 500
- Quantity of Bagels: 140
- Profit from Donuts: [tex]\( 500 \times 0.50 = 250 \)[/tex]
- Profit from Bagels: [tex]\( 140 \times 0.75 = 105 \)[/tex]
- Total Profit for Choice B: [tex]\( 250 + 105 = 355.0 \)[/tex]
#### Choice C:
- Quantity of Donuts: 500
- Quantity of Bagels: 40
- Profit from Donuts: [tex]\( 500 \times 0.50 = 250 \)[/tex]
- Profit from Bagels: [tex]\( 40 \times 0.75 = 30 \)[/tex]
- Total Profit for Choice C: [tex]\( 250 + 30 = 280.0 \)[/tex]
### Comparing the Profits:
- Profit for Choice A: 352.5
- Profit for Choice B: 355.0
- Profit for Choice C: 280.0
From these calculations, Choice B yields the highest profit of \$355.0.
Thus, the choice that yields the largest profit is Choice B.
