Business: Food Truck

The Food Truck Business Challenge 🌮🚚

A local food truck owner is optimizing their daily operations to maximize profit. The number of customers they serve per day depends on the price they set for their best-selling item, gourmet tacos.

Through past sales, they found that if they charge $5 per taco, they sell 200 tacos per day. However, for every $0.50 increase in price, they lose 10 customers.

Mathematical Model:

Let x be the number of $0.50 increases in price. The price of each taco can be written as:

The number of tacos sold per day becomes:

Revenue is given by:

Open-Ended Inquiry Questions:

1. Understanding the Situation: What does each part of the equation represent in the real-world context of the food truck business?
   
   

2. Optimization Challenge: What price should the food truck charge per taco to maximize revenue? Show how you determine this mathematically. How many tacos will be sold at this optimal price?
   
   

3. Beyond Revenue – Business Thinking: What other factors (besides revenue) should the owner consider when setting their price? How could this be modeled mathematically?
   
   

4. Entrepreneurial Extension: Suppose the owner wants to increase their daily revenue target by offering a special discount to boost customer engagement. How might you adjust the model to reflect this strategy?