To determine the vendor's profit for that day, we need to calculate his total revenue, total costs, and then the profit by subtracting the total costs from the total revenue.
Step 1: Calculate Total Revenue
The vendor sells 80 hotdogs at $20 each.
\[ \text{Total Revenue} = \text{Number of Hotdogs Sold} \times \text{Price per Hotdog} \] \[ \text{Total Revenue} = 80 \times 20 = 1600 \text{ dollars} \]
Step 2: Calculate Total Costs
2.1 Raw Materials
The vendor spends $12 on raw materials for each hotdog made.
\[ \text{Raw Material Cost} = \text{Number of Hotdogs Made} \times \text{Cost per Hotdog} \] \[ \text{Raw Material Cost} = 100 \times 12 = 1200 \text{ dollars} \]
2.2 Packing Costs
The vendor spends $1.00 on packing each hotdog.
\[ \text{Packing Cost} = \text{Number of Hotdogs Made} \times \text{Packing Cost per Hotdog} \] \[ \text{Packing Cost} = 100 \times 1 = 100 \text{ dollars} \]
2.3 Monthly Fixed Costs
These costs are fixed regardless of the number of hotdogs sold.
\[ \text{Monthly Fixed Costs} = 50 + 20 + 10 = 80 \text{ dollars} \]
2.4 Calculate Daily Fixed Costs
To get the daily fixed costs, we divide the monthly fixed costs by the number of days in the month.
\[ \text{Daily Fixed Costs} = \frac{\text{Monthly Fixed Costs}}{30} = \frac{80}{30} \approx 2.67 \text{ dollars} \]
2.5 Lost Sales
With 100 hotdogs prepared and only 80 sold, the vendor has 20 unhappy customers.
\[ \text{Lost Sales Cost} = \text{Number of Lost Sales} \times \text{Cost of Unhappiness per Customer} \] \[ \text{Lost Sales Cost} = 20 \times 1 = 20 \text{ dollars} \]
2.6 Leftover Hotdogs
He has 20 leftover hotdogs which he can sell at $5 each.
\[ \text{Revenue from Leftover Hotdogs} = \text{Number of Leftover Hotdogs} \times \text{Selling Price per Leftover Hotdog} \] \[ \text{Revenue from Leftover Hotdogs} = 20 \times 5 = 100 \text{ dollars} \]
Step 3: Calculate Total Costs
Now, we can sum up all the costs.
\[ \text{Total Costs} = \text{Raw Material Cost} + \text{Packing Cost} + \text{Daily Fixed Costs} + \text{Lost Sales Cost} - \text{Revenue from Leftover Hotdogs} \] \[ \text{Total Costs} = 1200 + 100 + 2.67 + 20 - 100 = 1222.67 \text{ dollars} \]
Step 4: Calculate Profit
Finally, we can calculate the profit.
\[ \text{Profit} = \text{Total Revenue} - \text{Total Costs} \] \[ \text{Profit} = 1600 - 1222.67 = 377.33 \text{ dollars} \]
Conclusion
The vendor’s profit for that day is $377.33.