Adele Weiss manages the campus flower shop. Flowers must be ordered three days i
ID: 450698 • Letter: A
Question
Adele Weiss manages the campus flower shop. Flowers must be ordered three days in advance from her supplier in Mexico. Although Valentine’s Day is fast approaching, sales are almost entirely last-minute, impulse purchases. Advance sales are so small that Weiss has no way to estimate the probability of low (25 dozen), medium (60 dozen), or high (130 dozen) demand for red roses on the big day. She buys roses for $15 per dozen and sells them for $40 per dozen. Construct a payoff table. Which decision is indicated by each of the following decision criteria? a. Maximin b. Maximax c. Laplace d. Minimax regret
Explanation / Answer
Profit = (Selling price * Demand) - (Cost price* No of dozens ordered)
Selling price = $40 per dozen
Cost price = $15 per dozen
=(40*25)-(15*25)
= 1000-375= $625
=(40*25)-(15*25)
= 1000-375= $625
=(40*25)-(15*25)
= 1000-375= $625
=(40* 25)- (15*60)
= 1000-900= $100
=(40* 60)- (15*60)
= 2400-900= $1500
=(40* 60)- (15*60)
= 2400-900=$1500
=(40*25)-(15*130)
=1000-1950=- $950
=(40*60)-(15*130)
=2400-1950= $450
=(40*130)-(15*130)
=5200-1950=$3250
Payoff table:
$625
625
$625
$100
$1500
$1500
- $950
$450
$3250
a) Maximin: The maximin payoff criterion is a pessimistic payoff criterion. We will do the following for this criteria
Find the minimum payoff for each section and choose the payoff that has the highest among these minimum payoffs.
$625 , $100, -$950 are the minimum payoff for each section and among them 625 is the highest.
Under Maxmin critera they should order 25 dozens where Demand is Low
b. Maximax : The maximax payoff criterion is an optimistic payoff criterion. We will do the following for this criteria
Find the maximum payoff for each section and choose the payoff that has the highest among these maximum payoffs.
625, 1500 and 3250 are the maximum payoff and 3250 is the maximum payoff among them.
Under Maximax they should order 130 Dozens
c. Laplace Criteria: The LaPlace criterion or the equal likelihood weights each state of nature equally assuming that the states of nature are equally likely to occur.
In this problem we have three states we assaign 0.333 to each one.
Now we will multiply these weights by each payoff for each decision and select the alternative which is having
maximum of these weighted values.
Order 25 Dozens = 0.333 * 625 + 0.333*625 + 0.333*625 = $625
Order 60 Dozens = 0.333 * 100+ 0.333*1500+ 0.333*1500= $1033.3
Order 130 Dozens=0.333 * (-950)+ 0.333*450 + 0.333*3250= $ 916.66
Among the above alternatives , Under Laplace criteria they should order 60 Dozens
d. Minimax regret: In this criteria we selects the maximum payoff under each state of nature and then all other payoffs under the respective states of nature are to be subtracted from these amounts
$625- $625=0
$1500-$625=$875
$3250-$625=$2625
$625-$100=$525
$1500- $1500=0
$3250-$1500=$1750
$625-(- $950)=$1575
$1500-$450=$1050
$3250-$3250=0
From the above table Maximum from each alternative are $2625, $1750, $1575. Among them $1575 is the minimum. So under Minimax regret they should order 130 dozens
Alternative/Demand Low(25 dozens) Medium(60 dozens) High(130 dozens) Order 25 dozens=(40*25)-(15*25)
= 1000-375= $625
=(40*25)-(15*25)
= 1000-375= $625
=(40*25)-(15*25)
= 1000-375= $625
Order 60 dozens=(40* 25)- (15*60)
= 1000-900= $100
=(40* 60)- (15*60)
= 2400-900= $1500
=(40* 60)- (15*60)
= 2400-900=$1500
Order 130 dozens=(40*25)-(15*130)
=1000-1950=- $950
=(40*60)-(15*130)
=2400-1950= $450
=(40*130)-(15*130)
=5200-1950=$3250
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