A bagel shop sells different kinds of bagels: onion, chocolate chip, sunflower, and wheat. The selling price for all bagels is $0.50 except for the chocolate chip which are $0.55. 1. How can we represent this information as a vector? Call this result P. 2. Each bagel costs a different amount to produce. We can display this information in an expense vector E = (0.32,0.38, 0.29, 0.27). Let I = (11, 12, 13, 14) be the inventory vector which lists the number available of each kind of bagel and let C = (C₁, C2, C3, C4) represent the consumption vector (ie, the vector listing the number of bagels sold each day). What do the following expressions mean? LI-C II. C -0.8Ī III. P- É 3. How could you compute the revenue (ie, gross income) for the day?
A bagel shop sells different kinds of bagels: onion, chocolate chip, sunflower, and wheat. The selling price for all bagels is $0.50 except for the chocolate chip which are $0.55. 1. How can we represent this information as a vector? Call this result P. 2. Each bagel costs a different amount to produce. We can display this information in an expense vector E = (0.32,0.38, 0.29, 0.27). Let I = (11, 12, 13, 14) be the inventory vector which lists the number available of each kind of bagel and let C = (C₁, C2, C3, C4) represent the consumption vector (ie, the vector listing the number of bagels sold each day). What do the following expressions mean? LI-C II. C -0.8Ī III. P- É 3. How could you compute the revenue (ie, gross income) for the day?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 81E
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![### Bagel Shop Sales and Profits Analysis
A bagel shop sells different kinds of bagels: onion, chocolate chip, sunflower, and wheat. The selling price for all bagels is $0.50 except for the chocolate chip which are $0.55.
### 1. Representing Sales Information as a Vector
How can we represent this information as a vector? We call this result \( \vec{P} \).
### 2. Expense and Consumption Vectors
Each bagel costs a different amount to produce. We can display this information in an expense vector \( \vec{E} = (0.32, 0.38, 0.29, 0.27) \).
Let \( \vec{I} = \langle I_1, I_2, I_3, I_4 \rangle \) be the inventory vector which lists the number available of each kind of bagel, and let \( \vec{C} = \langle C_1, C_2, C_3, C_4 \rangle \) represent the consumption vector (i.e., the vector listing the number of bagels sold each day).
**What do the following expressions mean?**
1. \( \vec{I} - \vec{C} \)
2. \( \vec{C} - 0.8 \vec{I} \)
3. \( \vec{P} - \vec{E} \)
To explain further:
1. \( \vec{I} - \vec{C} \): This expression represents the remaining inventory of each type of bagel at the end of the day.
2. \( \vec{C} - 0.8 \vec{I} \): This could represent the comparison of sold bagels against 80% of the initial inventory, potentially evaluating sales performance.
3. \( \vec{P} - \vec{E} \): This expression indicates the profit per bagel type, subtracting the production cost from the selling price.
### 3. Computing Revenue (Gross Income) for the Day
To compute the revenue for the day, sum the products of the selling price and the number of each type of bagel sold:
\[ \text{Revenue} = \sum ( \text{Selling Price} \times C_i ) \]
Where \( C_i \) is the number sold of](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8529e3ed-ff5a-4ce8-871f-01aea8265043%2Ffb3b06aa-4794-4d98-86e8-af44483ff76a%2Fgt3motr_processed.png&w=3840&q=75)
Transcribed Image Text:### Bagel Shop Sales and Profits Analysis
A bagel shop sells different kinds of bagels: onion, chocolate chip, sunflower, and wheat. The selling price for all bagels is $0.50 except for the chocolate chip which are $0.55.
### 1. Representing Sales Information as a Vector
How can we represent this information as a vector? We call this result \( \vec{P} \).
### 2. Expense and Consumption Vectors
Each bagel costs a different amount to produce. We can display this information in an expense vector \( \vec{E} = (0.32, 0.38, 0.29, 0.27) \).
Let \( \vec{I} = \langle I_1, I_2, I_3, I_4 \rangle \) be the inventory vector which lists the number available of each kind of bagel, and let \( \vec{C} = \langle C_1, C_2, C_3, C_4 \rangle \) represent the consumption vector (i.e., the vector listing the number of bagels sold each day).
**What do the following expressions mean?**
1. \( \vec{I} - \vec{C} \)
2. \( \vec{C} - 0.8 \vec{I} \)
3. \( \vec{P} - \vec{E} \)
To explain further:
1. \( \vec{I} - \vec{C} \): This expression represents the remaining inventory of each type of bagel at the end of the day.
2. \( \vec{C} - 0.8 \vec{I} \): This could represent the comparison of sold bagels against 80% of the initial inventory, potentially evaluating sales performance.
3. \( \vec{P} - \vec{E} \): This expression indicates the profit per bagel type, subtracting the production cost from the selling price.
### 3. Computing Revenue (Gross Income) for the Day
To compute the revenue for the day, sum the products of the selling price and the number of each type of bagel sold:
\[ \text{Revenue} = \sum ( \text{Selling Price} \times C_i ) \]
Where \( C_i \) is the number sold of
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