Complete Problem 8-3, 8-4 and 8-6

Complete Problem 8-3. Add this additional constraint: Total Number of Workers to Start the Shifts must be less than or equal to 31.

Complete Problem 8-4.

Complete Problem 8-6.

Use Excel's Solver to complete the problems.

Use one Excel spreadsheet file for the calculations and explanations, with one worksheet per problem. Use the problem number for each worksheet name. Cells should contain the formulas (i.e., if a formula was used to calculate the entry in that cell).






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 3am, 7am, 11am, 3pm, 7pm, or 11pm, 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 Xi equal the number of waiters and busboys beginning work in time period i, where i =1,2,3,4,5,6.)

PERIOD TIME # 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


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 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.

Feed Mix
Diet Oat Enriched Mineral Min Daily
Requirement Product Grain Product Requirement
(Ingredients) (Units/LB) (Units/LB) (Units/LB) (Units)
A 2 3 1 6
B 0.5 1 0.5 2
C 3 5 6 9
D 1 1.5 2 8
E 0.5 0.5 1.5 5
Cost/lb 0.09 0.14 0.17


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 cost of these, the audience reached by each type of ad, and the maximum number available is shown in the following table:





Audience Maximum
Type of Ad Cost per ad Reached Number
TV 800 30000 10
Radio 400 22000 10
Billboards 500 24000 10
Newspapers 100 8000 10

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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