The chart below shows a production possibility schedule for a pastry shop that makes $0.50 profit per donut and $0.75 profit per bagel.
Which choice yields the largest profit?
| Choice | Quantity of Donuts | Quantity of Bagels |
|---|---|---|
| A | 600 | 70 |
| B | 500 | 140 |
| C | 500 | 40 |
Answer (2)
The calculations of profits indicate that Choice B, with a profit of $355.00, yields the largest profit compared to the other choices. Therefore, the best choice for maximizing profit in this scenario is Choice B. In summary, the profits were $352.50 for Choice A, $355.00 for Choice B, and $280.00 for Choice C.
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Calculate the profit for Choice A: Profit A = ( 600 × $0.50 ) + ( 70 × $0.75 ) = $352.50
Calculate the profit for Choice B: Profit B = ( 500 × $0.50 ) + ( 140 × $0.75 ) = $355.00
Calculate the profit for Choice C: Profit C = ( 500 × $0.50 ) + ( 40 × $0.75 ) = $280.00
Choice B yields the largest profit: Choice B
Explanation
Problem Analysis We are given a production possibility schedule for a pastry shop and asked to determine which choice of donut and bagel production yields the largest profit. We are given that the profit per donut is $0.50 and the profit per bagel is $0.75. We need to calculate the total profit for each choice and then compare them to find the maximum profit.
Profit Calculation Formula To find the profit for each choice, we will use the formula: Total Profit = ( Quantity of Donuts × Profit per Donut ) + ( Quantity of Bagels × Profit per Bagel )
Profit for Choice A Let's calculate the profit for Choice A: Profit A = ( 600 × $0.50 ) + ( 70 × $0.75 ) = $300 + $52.50 = $352.50
Profit for Choice B Now, let's calculate the profit for Choice B: Profit B = ( 500 × $0.50 ) + ( 140 × $0.75 ) = $250 + $105 = $355.00
Profit for Choice C Next, let's calculate the profit for Choice C: Profit C = ( 500 × $0.50 ) + ( 40 × $0.75 ) = $250 + $30 = $280.00
Comparison and Conclusion Comparing the profits for each choice, we have: Profit A = $352.50 Profit B = $355.00 Profit C = $280.00
Since $355.00 > $352.50 > $280.00, Choice B yields the largest profit.
Examples
Understanding production possibilities and profit maximization is crucial for businesses. For example, a bakery can use this analysis to decide how many cakes and cookies to bake to maximize their daily profit, given their resources and the market demand for each product. This helps in making informed decisions about resource allocation and production planning.
