A Las Vegas supermarket bakery must decide how many wedding cakes to prepare for the upcoming weekend. Cakes cost $33 each to make, and they sell for $60 each. Unsold cakes are reducedto half-price on Monday, and typically one-third of those are sold. Any that remain are donated toa nearby senior center. Analysis of recent demand resulted in the following table:Demand 0 1 2 3Probability .15 .35 .30 .20How many cakes should be prepared to maximize expected profit?a. Use the ratio method.b. Use the tabular method (see Table 13.3). TABLE 13.3Expected cost for each possible outcomeAnd the demand probabilities areIf thestockingThe expectedcost will be23prob. = .20prob. =.40prob. = .30prob. =.10level is1 unit short .40(1)($4,200) = $1,680S=D2 units short .30(2)3 units short .10(3)$0($4,200) = $2,520($4,200) = $1,260$5,4601-unit excess .20(1)($800) = $1602 units short .10(2)($4,200) = $840S=D1 unit short .30(1)($4,200) = $1,260$0$2,2602-unit excess .20(2)($800) = $3201-unit excess .40(1)($800) = $320S=D1 unit short .10(1)($4,200) = $420$0$1,0602-unit excess .40(2)($800) = $6401-unit excess .30(1)($800) = $2403-unit excess .20(3)S=D($800) = $480$0$1,360

a. According to the given information: The calculation of number of spares to order:

Answered: TABLE 13.3 Expected cost for each…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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A Las Vegas supermarket bakery must decide how many wedding cakes to prepare for the upcoming weekend. Cakes cost $33 each to make, and they sell for $60 each. Unsold cakes are reduced
to half-price on Monday, and typically one-third of those are sold. Any that remain are donated to
a nearby senior center. Analysis of recent demand resulted in the following table:
Demand 0 1 2 3
Probability .15 .35 .30 .20
How many cakes should be prepared to maximize expected profit?
a. Use the ratio method.
b. Use the tabular method (see Table 13.3).

TABLE 13.3
Expected cost for each possible outcome
And the demand probabilities are
If the
stocking
The expected
cost will be
2
3
prob. = .20
prob. =.40
prob. = .30
prob. =.10
level is
1 unit short .40(1)
($4,200) = $1,680
S=D
2 units short .30(2)
3 units short .10(3)
$0
($4,200) = $2,520
($4,200) = $1,260
$5,460
1-unit excess .20(1)
($800) = $160
2 units short .10(2)
($4,200) = $840
S=D
1 unit short .30(1)
($4,200) = $1,260
$0
$2,260
2-unit excess .20(2)
($800) = $320
1-unit excess .40(1)
($800) = $320
S=D
1 unit short .10(1)
($4,200) = $420
$0
$1,060
2-unit excess .40(2)
($800) = $640
1-unit excess .30(1)
($800) = $240
3-unit excess .20(3)
S=D
($800) = $480
$0
$1,360

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