1. The famous Y.S Chang Restaurant is open 24 hours a day. Waiters and busboys report for duty at 3 am, 7 am, 11am, 3pm, 7pm or 11pm, and each works an 8-hour shift. The following table shows the minimum number of worker needed during the six periods into which the day is divided. Chang's scheduling problem is to determine how many waiters and busboys should report for work at the start of each time period to minimize the total staff required for one day's operation.( Hint: let xi equal the number of waiter and busboys beginning work in time period I, where i , 2,3,4,5,6.) Add this additional constraint - Total number of workers to start the shift must be less than or equal to 31.
PERIOD TIME NUMBER OF WAITERS AND BUSBOYS REQUIRED
1 3AM-7AM 3
2 7AM-11AM 12
3 11AM-3PM 16
4 3PM-7PM 9
5 7PM-11PM 11
6 11PM-3AM 4
2. The Battery Park Stable feeds and houses the horses used to pull tourists-filled carriages through the streets of Charleston's historic waterfront area. The stable owner, an ex-racehorse trainer, recognizes the need to set a nutritional diet for the horses in his care. At the same time, he would like to keep the overall daily cost of feed to a minimum. The feed mixes available for the horses' diet are an oat product, a highly enriched grain, and a mineral product. Each of these mixes contains a certain amount of five ingredients needed daily to keep the average horse healthy. The table below shows the minimum requirements, units of each ingredient per pound of feed mix, and costs for the three mixes. In addition, the stable owner is aware that an overfed horse is a sluggish worker. Consequently, he determines that 6 pounds of feed per day are the most that nay horse needs to function properly. Formulate this problem and solve for the optimal daily mix of the three feeds.
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Diet Requirements
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Oat Product (units/lb.
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Enriched Grain (units/lb.
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Mineral Product (units/lb.)
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Minimum Daily Requirements (units)
|
|
A
|
2
|
3
|
1
|
6
|
|
B
|
.5
|
1
|
.5
|
2
|
|
C
|
3
|
5
|
6
|
9
|
|
D
|
1
|
1.5
|
2
|
8
|
|
E
|
.5
|
.5
|
1.5
|
5
|
|
Cost/lb.
|
.09
|
.14
|
.17
|
|
3. Eddie Kelly is running for reelection as mayor of a small town in Alabama. Jessica Martinez, Kelly's campaign manager during this election, is planning the marketing campaign, and there is some stiff competition. Martinez has selected four ways to advertise: television ads, radio ads, billboards, and newspaper ads. The costs of these, the audience reached by each type of ad, and the maximum number available is shown in the following table:
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Type of Ad
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Cost per Ad
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Audience reached/Ad
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Maximum Number
|
|
TV
|
$800
|
30,000
|
10
|
|
Radio
|
$400
|
22,000
|
10
|
|
Billboards
|
$500
|
24,000
|
10
|
|
Newspaper
|
$100
|
8,000
|
10
|