Question 8-3 (Restaurant work scheduling problem). The famous Y. S. Chang Restaurant is open 24 hours

8-3 (Restaurant work scheduling problem).
The famous Y. S. Chang Restaurant is open 24 hours a day. Waiters and busboys report for duty at 3 A .M ., 7 A .M .,11 A .M ., 3 P .M ., 7 P .M ., or 11 P .M ., and each works an 8-hour shift. The following table shows the minimum number of workers 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 equal the number of waiters and busboys beginning work in time period i , where i = 1, 2, 3, 4, 5, 6.)

NUMBER OF WAITERS
PERIOD TIME AND BUSBOYS REQUIRED
1 3 A.M.–7 A.M. 3
2 7 A.M.–11 A.M. 12
3 11 A.M.–3 P.M. 16
4 3 P.M.–7 P.M. 9
5 7 P.M.–11 P.M. 11
6 11 P.M.–3 A.M 4

(a) Add this additional constraint: Total Number of Workers to Start the Shifts must be less than or equal to 31.

8-4 (Animal feed mix problem) The Battery Park Stable feeds and houses the horses used to pull tourist-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 on this page shows these 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 any horse needs to function properly. Formulate this problem and solve for the optimal daily mix of the three feeds. Please see attached excel spead sheet for original data from problem.

8-6 Eddie Kelly is running for re-election 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 of each is shown in the following table:

See attached spreadsheet for table

In addition, Martinez has decided that there should be at least six ads on TV or radio or some combination of those two. The amount spent on billboards and newspapers together must not exceed the amount spent on TV ads. While fundraising is still continuing, the monthly budget for advertising has been set at $15,000. How many ads of each type should be placed to maximize the total number of people reached?

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