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

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SUMMARY

The discussion centers on the calculation of the dot product of two vectors, A and P, where A represents the quantities of items sold by a street vendor, specifically hamburgers, hot dogs, and soft drinks, and P represents their respective prices. The dot product A * P is calculated as 2*a + 1.5*b + 1*c, yielding a scalar that signifies the total revenue generated from sales. The interpretation of this calculation is that it quantifies the total income based on the number of items sold multiplied by their prices, effectively translating sales data into a monetary value.

PREREQUISITES
  • Understanding of vector mathematics, specifically dot products.
  • Familiarity with basic algebraic expressions and operations.
  • Knowledge of how to interpret vectors in a real-world context.
  • Basic understanding of revenue calculations in sales scenarios.
NEXT STEPS
  • Study vector operations, focusing on the dot product and its applications in real-world scenarios.
  • Explore revenue calculation methods in business mathematics.
  • Learn about the significance of scalar results from vector operations.
  • Investigate practical examples of vector applications in economics and sales analysis.
USEFUL FOR

Students studying mathematics, particularly those interested in vector operations, as well as business analysts and sales professionals looking to understand revenue calculations through mathematical models.

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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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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
 

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