Mayor Porky Pigg has to decide whether or not to start arecycling program in Got
ID: 2916883 • Letter: M
Question
Mayor Porky Pigg has to decide whether or not to start arecycling program in Got-ham City. The fixed
cost for the program is $60,000 per week. Each household thatparticipates generates garbage that results
in $0.50 of revenue per week to the city (you can assume everyhousehold either participates every week
or it does not participate at all). Mayor Pigg believes thatthere will either be a high participation rate
(30% of all households), a medium participation rate (20% of allhouseholds), a low participation rate
(10% of all households), or a minimal participation rate (5% ofall households). Mayor Pigg estimates the
probabilities of the participation rates as P(high) = 0.35;P(medium) = 0.3; P(low) = 0.25; and P(minimal)
= 0.1. There are 1,000,000 households in Got-ham City. The mayorwishes to choose the strategy that
maximizes the expected net revenue.
(a) Based on the information as given, should Mayor Pigg startthe recycling program or
should he not start it? What is the expected net revenue perweek from the optimal choice?
(b) A preliminary survey was performed. 100 households wereasked if they would or if
they would not participate in the recycling program. 12households said they would participate and 88
said they would not.
(1) If the participation rate is high, what is the probabilitythat a survey of 100
households would yield 12 saying they would participate and 88saying they would not
participate?
(2) If the participation rate is medium, what is the probabilitythat a survey of 100
households would yield 12 saying they would participate and 88saying they would not
participate?
(3) If the participation rate is low, what is the probabilitythat a survey of 100
households would yield 12 saying they would participate and 88saying they would not
participate?
(4) If the participation rate is minimal, what is theprobability that a survey of 100
households would yield 12 saying they would participate and 88saying they would not
participate?
(5) Taking into account the results of the preliminary survey,determine whether or
not Mayor Pigg should or should not start the recycling program,and determine the expected net
revenue per week from the optimal choice.
Explanation / Answer
(a)Let R= revenue/week. then E[R]=60,000-(.5)(1,000,000)[.3(.35)+.2(.3)+.1(.25)+.05(.1)] =-$37,500 (loses money) So no, he should not start theprogram base on expected revenue from his assignedprobabilities. (b)Sample of 100 yields 12 interested 88 not interested. This is a binomial distribution with n=100 and x=12. Therefore, P(12)=C(100,12)p12(1-p)88 where C=number of combination of 12 out of 100 sayinginterested.(1)at high participation p=.3 and P(12)=.000013 (2)at medium participation p=.2 and P(12)=.012759 (3)at low participation p=.1 and P(12)=.098788 (4)at minimal participation p=.05 and P(12)=.00289 Therefore, from the survey low participation is most likely.Expected revenue per week would be E[R]=60,000-.5(.1)(1,000,000=$10,000/week. So themayor should do it based on the sample.