A small coastal town has a 1-kilometer-long beach represented by D = [0,1000]. During summer months, there are two ice-cream trucks operated by Jack and Sue, which sell the same brand of ice cream at a price of p. During the day, there are 250 people on the beach who are uniformly distributed (along the beach). Jack and Sue have no fixed costs, but they have a unit cost of c such that p > c. They each drive their ice-cream trucks to the beach early in the morning and choose a location, Tsue and TJack, respectively, in D. Each person on the beach buys one ice cream per day from the truck closest to his/her location on the beach (if the person is equidistant to the trucks, he/she picks one randomly). 1. Drawing a straight line depicting the beach, choose two arbitrary locations on it such that T Jack
A small coastal town has a 1-kilometer-long beach represented by D = [0,1000]. During summer months, there are two ice-cream trucks operated by Jack and Sue, which sell the same brand of ice cream at a price of p. During the day, there are 250 people on the beach who are uniformly distributed (along the beach). Jack and Sue have no fixed costs, but they have a unit cost of c such that p > c. They each drive their ice-cream trucks to the beach early in the morning and choose a location, Tsue and TJack, respectively, in D. Each person on the beach buys one ice cream per day from the truck closest to his/her location on the beach (if the person is equidistant to the trucks, he/she picks one randomly). 1. Drawing a straight line depicting the beach, choose two arbitrary locations on it such that T Jack
Managerial Economics: A Problem Solving Approach
5th Edition
ISBN:9781337106665
Author:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Chapter7: Economies Of Scale And Scope
Section: Chapter Questions
Problem 7.5IP
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![A small coastal town has a 1-kilometer-long beach represented by D = [0,1000]. During
summer months, there are two ice-cream trucks operated by Jack and Sue, which sell the
same brand of ice cream at a price of p. During the day, there are 250 people on the beach
who are uniformly distributed (along the beach). Jack and Sue have no fixed costs, but they
have a unit cost of c such that p > c. They each drive their ice-cream trucks to the beach
early in the morning and choose a location, Tsue and Tjack ,respectively, in D. Each person on
the beach buys one ice cream per day from the truck closest to his/her location on the
beach (if the person is equidistant to the trucks, he/she picks one randomly).
1. Drawing a straight line depicting the beach, choose two arbitrary locations on it
such that Tjack < TsSue (locations for the ice-cream trucks). Given the description from
above, provide an algebraic definition of which customers (depending on their
positions on the beach) buy from which truck. Show on your picture.
2. For any given locations such that Tjack < T sue , What is the profit of each truck per day
as a function of Tjack and Tsue ? Explain. What is the total daily profit of the two
trucks?
3. If the management of the beach chooses the locations for the ice-cream trucks with
the goal of minimizing the average walking distance for the customers to the nearest
truck, which location(s) would they choose? Explain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd72e8838-7715-4bdc-a296-a5989c0a56c0%2F1854b76d-f8ec-4c03-8803-b18434a00d86%2Fi3dr8e2o_processed.png&w=3840&q=75)
Transcribed Image Text:A small coastal town has a 1-kilometer-long beach represented by D = [0,1000]. During
summer months, there are two ice-cream trucks operated by Jack and Sue, which sell the
same brand of ice cream at a price of p. During the day, there are 250 people on the beach
who are uniformly distributed (along the beach). Jack and Sue have no fixed costs, but they
have a unit cost of c such that p > c. They each drive their ice-cream trucks to the beach
early in the morning and choose a location, Tsue and Tjack ,respectively, in D. Each person on
the beach buys one ice cream per day from the truck closest to his/her location on the
beach (if the person is equidistant to the trucks, he/she picks one randomly).
1. Drawing a straight line depicting the beach, choose two arbitrary locations on it
such that Tjack < TsSue (locations for the ice-cream trucks). Given the description from
above, provide an algebraic definition of which customers (depending on their
positions on the beach) buy from which truck. Show on your picture.
2. For any given locations such that Tjack < T sue , What is the profit of each truck per day
as a function of Tjack and Tsue ? Explain. What is the total daily profit of the two
trucks?
3. If the management of the beach chooses the locations for the ice-cream trucks with
the goal of minimizing the average walking distance for the customers to the nearest
truck, which location(s) would they choose? Explain.
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