Street Vendor's Daily Sales: Understanding A * P Dot Product

  • Thread starter Calpalned
  • Start date
In summary: So the dot product is just a way of finding the total cost of all the items sold by multiplying the number sold by the price. In summary, the dot product of A and P represents the total cost of the items sold by the street vendor, where A is a vector representing the number of hamburgers, hot dogs, and soft drinks sold and P is a vector representing the price of each item. It is calculated by multiplying the number of each item sold by its corresponding price and adding them together. This is a way of finding the total cost of all the items sold.
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Homework Statement


A street vendor sells a hamburgers, b hot dogs, and c soft drinks on a given day. He charges $2 for a hamburger, $1.50 for a hot dog, and $1 for a soft drink. If A = <a, b, c>, and P = <2, 1.5, 1> , what is the meaning of the dot product A * P

Homework Equations


- Dot product of <x, y, z> and <a, b, c> is xa + yb + zc
- Two vectors multiply to become a scalar.

The Attempt at a Solution


I have no clue what the significance of the dot product in this situation is. Additionally, I don't see how $1.50 and nor the number of hot dogs are vectors.
 
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  • #2
Imagine they didn't say anything about vectors and just gave you the equation "2*a + 1.5*b + 1*c", would you know what it describes? You're multiplying the price of something by the number of those things you sold. What does that mean in real life?As for the vectors:

Without all this business about hotdogs and money, do you know how to interpret <1, 2, 3>? It means that x = 1, y = 2, z = 3 in a traditional Euclidean space, right?

Now just imagine that instead of x, y, z we relabel them "x = number of hamburgers, y = number of hotdogs and z = number of soft drinks". In this case x = a, y = b, z = c so they form a vector <a, b, c>.

Do the same thing for the price. "x = price of a hamburger, y = price of a hotdog, z = price of a drink" then our vector is <2. 1.5, 1>.

Doing the dot product we get 2*a + 1.5*b + 1*c
 

1. What is the purpose of understanding the A * P dot product in relation to street vendor's daily sales?

The A * P dot product is a mathematical concept that allows us to determine the total sales made by a street vendor over a period of time. It helps us understand the relationship between the number of items sold (A) and the price of each item (P), and how it contributes to the vendor's daily sales.

2. How is the A * P dot product calculated?

The A * P dot product is calculated by multiplying the number of items sold (A) by the price of each item (P). This gives us the total sales made by the street vendor for that particular day.

3. Why is it important for a street vendor to understand the A * P dot product?

Understanding the A * P dot product allows a street vendor to track their daily sales and make informed decisions about their business. It also helps them identify which items are selling well and which ones are not, so they can adjust their prices or offerings accordingly.

4. How can the A * P dot product be used to improve a street vendor's business?

By understanding the A * P dot product, a street vendor can analyze their sales data and identify patterns or trends that can help them make strategic business decisions. For example, if the A * P dot product is consistently low on a particular day, the vendor can adjust their pricing or marketing strategies to increase sales.

5. Are there any limitations to using the A * P dot product for analyzing street vendor's sales?

While the A * P dot product is a useful tool for understanding street vendor's daily sales, it does not take into account other factors that may affect their business, such as location, competition, or weather. It should be used in conjunction with other data and observations to get a more comprehensive understanding of the vendor's sales performance.

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