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A College Student,Stan Ford,recently Took a Course in Operations Research

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A college student,Stan Ford,recently took a course in operations research.He now enjoys applying what he learned to optimize his personal decisions.He is analyzing one such decision currently,namely,how much money (if any)to take out of his savings account to buy $100 traveler's checks before leaving on a short vacation trip to Europe next summer.Stan already has used the money he had in his checking account to buy traveler's checks worth $1,200,but this may not be enough.In fact,he has estimated the probability distribution of what he will need as shown in the following table: A college student,Stan Ford,recently took a course in operations research.He now enjoys applying what he learned to optimize his personal decisions.He is analyzing one such decision currently,namely,how much money (if any)to take out of his savings account to buy $100 traveler's checks before leaving on a short vacation trip to Europe next summer.Stan already has used the money he had in his checking account to buy traveler's checks worth $1,200,but this may not be enough.In fact,he has estimated the probability distribution of what he will need as shown in the following table: If he turns out to have less than he needs,then he will have to leave Europe 1 day early for every $100 short.Because he places a value of $150 on each day in Europe,each day lost would thereby represent a net loss of $50 to him.However,every $100 traveler's check costs an extra $1.Furthermore,each such check left over at the end of the trip (which would be redeposited in the savings account)represents a loss of $2 in interest that could have been earned in the savings account during the trip,so he does not want to purchase too many.(a)Describe how this problem can be interpreted to be an inventory problem with uncertain demand for a perishable product.Also identify the unit cost of underordering and the unit cost of overordering.(b)Use Bayes' decision rule presented in Sec.16.2 of the textbook to determine how many additional $100 traveler's checks Stan should purchase to minimize his expected cost of underordering or overordering.(c)Recall that the stochastic single-period model for perishable products (as presented in Sec.18.7 of the textbook)finds that the optimal service level is Optimal service level = ,where C<sub>under </sub> is the unit cost of underordering and C<sub>over</sub> is the unit cost of overordering.Use this result and the table of probabilities to make Stan's decision.d)Draw a graph of the CDF of demand to show the application of the model in part (c)graphically. If he turns out to have less than he needs,then he will have to leave Europe 1 day early for every $100 short.Because he places a value of $150 on each day in Europe,each day lost would thereby represent a net loss of $50 to him.However,every $100 traveler's check costs an extra $1.Furthermore,each such check left over at the end of the trip (which would be redeposited in the savings account)represents a loss of $2 in interest that could have been earned in the savings account during the trip,so he does not want to purchase too many.(a)Describe how this problem can be interpreted to be an inventory problem with uncertain demand for a perishable product.Also identify the unit cost of underordering and the unit cost of overordering.(b)Use Bayes' decision rule presented in Sec.16.2 of the textbook to determine how many additional $100 traveler's checks Stan should purchase to minimize his expected cost of underordering or overordering.(c)Recall that the stochastic single-period model for perishable products (as presented in Sec.18.7 of the textbook)finds that the optimal service level is Optimal service level = A college student,Stan Ford,recently took a course in operations research.He now enjoys applying what he learned to optimize his personal decisions.He is analyzing one such decision currently,namely,how much money (if any)to take out of his savings account to buy $100 traveler's checks before leaving on a short vacation trip to Europe next summer.Stan already has used the money he had in his checking account to buy traveler's checks worth $1,200,but this may not be enough.In fact,he has estimated the probability distribution of what he will need as shown in the following table: If he turns out to have less than he needs,then he will have to leave Europe 1 day early for every $100 short.Because he places a value of $150 on each day in Europe,each day lost would thereby represent a net loss of $50 to him.However,every $100 traveler's check costs an extra $1.Furthermore,each such check left over at the end of the trip (which would be redeposited in the savings account)represents a loss of $2 in interest that could have been earned in the savings account during the trip,so he does not want to purchase too many.(a)Describe how this problem can be interpreted to be an inventory problem with uncertain demand for a perishable product.Also identify the unit cost of underordering and the unit cost of overordering.(b)Use Bayes' decision rule presented in Sec.16.2 of the textbook to determine how many additional $100 traveler's checks Stan should purchase to minimize his expected cost of underordering or overordering.(c)Recall that the stochastic single-period model for perishable products (as presented in Sec.18.7 of the textbook)finds that the optimal service level is Optimal service level = ,where C<sub>under </sub> is the unit cost of underordering and C<sub>over</sub> is the unit cost of overordering.Use this result and the table of probabilities to make Stan's decision.d)Draw a graph of the CDF of demand to show the application of the model in part (c)graphically. ,where Cunder is the unit cost of underordering and Cover is the unit cost of overordering.Use this result and the table of probabilities to make Stan's decision.d)Draw a graph of the CDF of demand to show the application of the model in part (c)graphically.

Definitions:

Opposition

Resistance or dissent, expressed in action or argument, against prevailing ideas, policies, or entities in power.

Martin Luther King

An American Baptist minister and activist who became the most visible spokesperson and leader in the civil rights movement from 1955 until his assassination in 1968.

Garbage Workers Strike

A labor strike involving sanitation workers who refuse to collect garbage, usually to protest for better wages, working conditions, or benefits.

Memphis

A city in the southwestern part of Tennessee, known for its influential strains of blues, soul, and rock 'n' roll music, as well as its historical significance in the civil rights movement.

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