Unformatted text preview: the evening are converted into clam chowder for lunch diners the following day. Sylvia estimates the salvage value of these clams at $2.00 per order not sold in the evening. a) What is the optimal number of clam dinners for Sylvia to buy if she wants to maximize her expected profit? We want the smallest value of the cumulative distribution, F ( x ) , such that
p " c 25 " 8 17
=
=
= 0.72727
p " s 25 " 2 22
So x = 4
F ( x) ! b) If Sylvia buys the number of clam dinners found in part (a), what is the expected number of dinners that she can sell? For this and the next two parts of this problem, the table at the end of the problem may be useful. 2.88 c) If Sylvia buys the number of clam dinners found in part (a), what is the expected number of dinners that are NOT sold at the end of the day? 1.12 6 of 8 pages IOE 491, Service Operations Management
Winter, 2012, IOE Dept, U. Michigan Name Place your name on all pages now! d) If Sylvia buys the number of clam dinners found in part (a), what is her expected profit? 2.88*25+1.12*2
4*8=42.24 7 of 8 pages IOE 491, Service Operations Management
Winter, 2012, IOE Dept, U. Michigan Name Place your name on all pages now! Problem 4: Period Number Carolyn’s Coffee Corner (CCC) is a popular coffee and Number Period Needed
pastry shop in town – some town. CCC is open for 1
5
7
3
business from 5 am to 11 pm every day. Carolyn’s 2
7
9
8
patronage varies over the course of the day, and 3
9
11
6
Carolyn has determined that she the number of 4
11
13
11
employees that she needs to have on duty during each 2 5
13
15
9
hour period is as given in the table to the right. 6
15
17
8
Carolyn relies heavily on the local student body for 7
17
19
9
employees and so each employee works only a six hour 8
19
21
8
(or 3 period) shift. 9
21
23
4
a) If Carolyn uses a naïve approach of scheduling employees to start at the beginning of period 1, then at the beginning of period 4 and then at the beginning of period 7 – in other words, she uses 3 non
overlapping shifts of 6 hours each – how many employees does she need each day? 8+11+9=28 b) What is the optimal number of employees for Carolyn to hire? 25 employees 8 of 8 pages...
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