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

[Calpalned]

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.

 

[O_o]

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