To calculate the profit the restaurant earned today, we need to consider the revenue generated from the sales of sandwiches, the costs incurred in making the sandwiches, and the costs associated with lost sales and leftover sandwiches.
Here's a breakdown of the calculations:
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Cost of Materials for Sandwiches:
- Number of sandwiches prepared: 200
- Cost per sandwich (raw materials): $6.00
- Total cost of raw materials: \[ 200 \text{ sandwiches} \times 6 \text{ dollars/sandwich} = 1200 \text{ dollars} \]
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Sales Revenue:
- Selling price per sandwich: $10.00
- Number of sandwiches sold: 200 (because they can only sell what they prepared)
- Total sales revenue: \[ 200 \text{ sandwiches} \times 10 \text{ dollars/sandwich} = 2000 \text{ dollars} \]
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Cost of Lost Sales:
- According to the problem, the restaurant could have sold 214 sandwiches, and they prepared only 200.
- Number of potential lost sales: \[ 214 - 200 = 14 \text{ sandwiches} \]
- Cost of lost sales: \[ 14 \text{ sandwiches} \times 5 \text{ dollars/sandwich} = 70 \text{ dollars} \]
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Leftover Sandwiches:
- Since they prepared 200 sandwiches and sold all of them, there are no leftover sandwiches.
- Revenue from leftover sandwiches: \[ 0 \text{ sandwiches} \times 3 \text{ dollars/sandwich} = 0 \text{ dollars} \]
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Total Costs:
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Total costs include raw material costs, rental, and insurance. However, since those are monthly costs and we want the profit for just one day, we should factor in the daily proportional costs of rental and insurance.
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Daily cost of rentals and insurance:
- Monthly rental: $1,046.00
- Monthly insurance: $294.00
- Daily rental cost: \[ \frac{1046}{25} = 41.84 \text{ dollars/day} \]
- Daily insurance cost: \[ \frac{294}{25} = 11.76 \text{ dollars/day} \]
- Total daily fixed costs: \[ 41.84 + 11.76 = 53.60 \text{ dollars} \]
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Total cost incurred today: \[ \text{Raw materials} + \text{Daily fixed costs} = 1200 + 53.60 = 1253.60 \text{ dollars} \]
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Profit Calculation:
- Profit today = Total Sales Revenue - Total Costs - Cost of Lost Sales
- Profit: \[ 2000 - (1253.60 + 70) = 2000 - 1323.60 = 676.40 \text{ dollars} \]
The restaurant earned a profit of $676.40 today.