8.3 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_x000d_
1 3AM-7AM 3_x000d_
2 7AM-11AM 12_x000d_
3 11AM-3PM 16_x000d_
4 3PM-7PM 9_x000d_
5 7PM-11PM 11_x000d_
6 11PM-3AM 4_x000d_
8.4 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. _x000d_
Diet Requirements_x000d_
Oat Product (units/lb._x000d_
Enriched Grain (units/lb._x000d_
Mineral Product (units/lb.)_x000d_
Minimum Daily Requirements (units)
A_x000d_
2_x000d_
3_x000d_
1_x000d_
6_x000d_
B_x000d_
.5_x000d_
1_x000d_
.5_x000d_
2_x000d_
C_x000d_
3_x000d_
5_x000d_
6_x000d_
9_x000d_
D_x000d_
1_x000d_
1.5_x000d_
2_x000d_
8_x000d_
E_x000d_
.5_x000d_
.5_x000d_
1.5_x000d_
5_x000d_
Cost/lb._x000d_
.09_x000d_
.14_x000d_
.17_x000d_
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Please remember that I need to know how to do this so I would really appreciate the formulas (equations) in excel._x000d_
8.6 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:
Type of Ad_x000d_
Cost per Ad_x000d_
Audience reached/Ad_x000d_
Maximum Number_x000d_
TV_x000d_
$800_x000d_
30,000_x000d_
10_x000d_
Radio_x000d_
$400_x000d_
22,000_x000d_
10_x000d_
Billboards_x000d_
$500_x000d_
24,000_x000d_
10_x000d_
Newspaper_x000d_
$100_x000d_
8,000_x000d_
10
