Few companies take the time to estimate the value of a good customer (and often spend little effort to keep one) Suppose that a customer at a restaurant spends, on average R per visit and comes F times each year (for example, if a customer purchases once every two years, then F= =05 The restaurant realizes a gross profit margin of M (expressed as a fraction) on the average bill for fod and drinks In addition, the fraction of customers defecting (not returning) each year is D 2 Complete parts a and b a. Develop a mathematical model to compute V, the gross profit during a customer's lifetime in doing business with the restaurant (this is often called the economic value of a customer) V= (rF•m) • (Simplify your answer) b. If the average purchase per visit is $40, the gross profit margin is 03 (that is, 30%) customers VIsit an average of five times each year and 40% of customers defect each year what is the economic value of the customer? The economic value of the customer is $ (Round to the nearest dollar as needed)
Few companies take the time to estimate the value of a good customer (and often spend little effort to keep one) Suppose that a customer at a restaurant spends, on average R per visit and comes F times each year (for example, if a customer purchases once every two years, then F= =05 The restaurant realizes a gross profit margin of M (expressed as a fraction) on the average bill for fod and drinks In addition, the fraction of customers defecting (not returning) each year is D 2 Complete parts a and b a. Develop a mathematical model to compute V, the gross profit during a customer's lifetime in doing business with the restaurant (this is often called the economic value of a customer) V= (rF•m) • (Simplify your answer) b. If the average purchase per visit is $40, the gross profit margin is 03 (that is, 30%) customers VIsit an average of five times each year and 40% of customers defect each year what is the economic value of the customer? The economic value of the customer is $ (Round to the nearest dollar as needed)
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
2)Solve for B see picture
![**Estimating the Economic Value of a Customer for a Restaurant**
Many companies strive to estimate the value of a loyal customer, though they might not always invest efforts in retaining them. Let's consider a scenario where a customer at a restaurant spends, on average, \( R \) dollars per visit and visits \( F \) times each year. For example, if a customer makes a purchase once every two years, then \( F = \frac{1}{2} = 0.5 \). The restaurant realizes a gross profit margin of \( M \) (expressed as a fraction) on the average bill for food and drinks. Additionally, a fraction \( D \) of customers do not return each year, known as the defection rate.
**Tasks:**
**a. Develop a Mathematical Model:**
To compute \( V \), the gross profit during a customer’s lifetime spent with the restaurant (often referred to as the economic value of a customer), we use the formula:
\[
V = \left(\frac{r \cdot F \cdot m}{d}\right)
\]
- **Simplify your answer.**
**b. Calculate the Economic Value:**
Given:
- The average purchase per visit is \( R = \$40 \).
- The gross profit margin is \( M = 0.3 \) (i.e., 30%).
- Customers visit on average \( F = 5 \) times each year.
- \( 40\% \) of customers defect each year, thus \( D = 0.4 \).
**Question:**
What is the economic value of the customer?
Be sure to round to the nearest dollar as needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6835fe2b-4dfe-4db0-80f6-f1ad78fce3f2%2F07b47ffc-67c3-4915-99b0-b09ebd2a0211%2Fy5ofgyn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Estimating the Economic Value of a Customer for a Restaurant**
Many companies strive to estimate the value of a loyal customer, though they might not always invest efforts in retaining them. Let's consider a scenario where a customer at a restaurant spends, on average, \( R \) dollars per visit and visits \( F \) times each year. For example, if a customer makes a purchase once every two years, then \( F = \frac{1}{2} = 0.5 \). The restaurant realizes a gross profit margin of \( M \) (expressed as a fraction) on the average bill for food and drinks. Additionally, a fraction \( D \) of customers do not return each year, known as the defection rate.
**Tasks:**
**a. Develop a Mathematical Model:**
To compute \( V \), the gross profit during a customer’s lifetime spent with the restaurant (often referred to as the economic value of a customer), we use the formula:
\[
V = \left(\frac{r \cdot F \cdot m}{d}\right)
\]
- **Simplify your answer.**
**b. Calculate the Economic Value:**
Given:
- The average purchase per visit is \( R = \$40 \).
- The gross profit margin is \( M = 0.3 \) (i.e., 30%).
- Customers visit on average \( F = 5 \) times each year.
- \( 40\% \) of customers defect each year, thus \( D = 0.4 \).
**Question:**
What is the economic value of the customer?
Be sure to round to the nearest dollar as needed.
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps

Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.Recommended textbooks for you


Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON

Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON


Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON

Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON

Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning

Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning

Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education