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A vendor prepares 100.00 hotdogs every day and sells at $22.00 /piece. For each hot dog, he spends $11.00 in the raw material. Additionally he spends $1.58 for packing each hotdog and monthly $51.00, $21.00, $9.00 as food truck rent, electricity and other expenses respectively. Lost sales are charged at $5.00 per lost sale. Leftover hotdogs can be sold for $3.

On a particular day in June 111.00 people came wanting to buy a hotdog. Determine the vendor’s profit for that day? Assume there are 30 days in the month.

1 answer

To calculate the vendor's profit for that day, we will follow these steps:

  1. Determine the revenue from hotdog sales.
  2. Calculate the total costs incurred by the vendor.
  3. Factor in losses from unmet demand and leftover hotdogs.
  4. Calculate the profit.

Step 1: Revenue from Hotdog Sales

The vendor sells each hotdog for $22.00 and had 111 customers.

  • Revenue = Number of sales × Price per hotdog
  • Revenue = 100 hotdogs × $22.00 = $2200.00 (since only 100 can be sold)

Step 2: Total Costs

  • Cost per hotdog (raw material + packing):

    • Raw material cost = $11.00
    • Packing cost = $1.58
    • Total cost per hotdog = $11.00 + $1.58 = $12.58

  • Total cost for 100 hotdogs:

    • Total cost for hotdogs = 100 × $12.58 = $1258.00

  • Fixed monthly costs (allocated per day):

    • Food truck rent = $51.00
    • Electricity = $21.00
    • Other expenses = $9.00
    • Total fixed costs = $51.00 + $21.00 + $9.00 = $81.00
    • Daily fixed costs = $81.00 / 30 days = $2.70 (approximately)

  • Total Costs for the Day = Total cost for hotdogs + Daily fixed costs

    • Total Costs = $1258.00 + $2.70 = $1260.70

Step 3: Lost Sales and Leftovers

  • Lost Sales:

    • The demand was for 111 hotdogs, but only 100 were sold.
    • Therefore, lost sales = 111 - 100 = 11 hotdogs
    • Loss from lost sales = 11 × $5.00 = $55.00

  • Leftover hotdogs:

    • All 100 hotdogs were sold, so there are no leftovers.
    • Revenue from leftovers = 0

Step 4: Calculate Profit

  • Total Revenue = $2200.00

  • Total Costs = $1260.70 + Lost Sales Loss = $1260.70 + $55.00 = $1315.70

  • Profit = Total Revenue - Total Costs

  • Profit = $2200.00 - $1315.70 = $884.30

Thus, the vendor's profit for that day is $884.30.