ARE 157
ANALYSIS FOR PRODUCTION MANAGEMENT
Homework 30ue Monday, Nov. 17th, at start
ofclass
Fall 2008
M.Whitney
(12) 1. At Luigi's, a cafe, the menu features a seafood pasta dish made with fresh scallops. Because the
ingtedients are purchased fresh in the afternoon, the cafe must plan in advance how many servings ofthis dish
will be prepared each evening.
The dish sells for $22.40, and costs $5.60 to prepare. Any dinners that are not sold are discarded and
bring in no revenue. Based on past sales experience, the fmn knows the probability ofserving various
quantities ofthis dish is as follows:
# ofdinners served
P(d)
P(O)
<20
0
21
.10
22
.15
23
.15
24
.2
25
.15
26
.15
27
.05
28
.05
29 or more
0
a.. Find P(D), the probability
of"stocking out", for each number ofdinners that
is
prepared. [Note: P(O) is
the probability that demand will be greater than or equal to the number ofdinners prepared].
b.
Calculate the expected profit or loss from the 21
st
dinner, and the 28
th
dinner. Now fmd the optimal
probability
ofstocking out. To
maximize
expected profit, how many dinners should be prepared each day?
c.
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 Spring '08
 WHITNEY
 labor force, baby world, Toy House, monthly beginning inventory

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