5 Probability questions/problems
ijeffer604
wk8homeworktemplate.xlsxP1
| Eagle Tavern | ||||||
| Yodel | Shotz | Rainwater | ||||
| Cost/Gallon | 1.5 | 0.9 | 0.5 | |||
| Selling price | 3 | 2.5 | 1.75 | |||
| profit | ||||||
| Capacity | 1 | 1 | 1 | = | 1000 | |
| Demand for Yodel | 1 | 0 | 0 | <= | 400 | |
| Demand for Shotz | 0 | 1 | 0 | <= | 500 | |
| Demand for Rainwater | 0 | 0 | 1 | <= | 300 | |
| # of Gallons | # of Gallons | # of Gallons | ||||
| Yodel | Shotz | Rainwater | ||||
| Decision Variables | ||||||
| Objective Function | ||||||
P2
| congressman’s district | ||||||
| Program | Votes/ Dollar | |||||
| Job training | 0.03 | |||||
| Parks | 0.08 | |||||
| Sanitation | 0.05 | |||||
| Mobile library | 0.03 | |||||
| Comments | ||||||
| Constraints | <= | 900000 | Job training | |||
| <= | 900000 | Parks | ||||
| <= | 900000 | Sanitation | ||||
| <= | 900000 | Mobile library | ||||
| <= | Parks <= Sanitation + Mobile Library | |||||
| >= | Job training >= Sanitation | |||||
| spending | = | 3000000 | all four job catagories | |||
| Decision Variables | Job training | |||||
| Parks | ||||||
| Sanitation | ||||||
| Mobile library | ||||||
| Objective | Maximize Votes |
P3
| Anna Broderick Lunch Menu | ||||||||||
| Calories | Iron | Protein | Carbo-hydrates | Fat (g/lb.) | Chol-esterol | Cost | ||||
| (per lb.) | (mg/lb.) | (g/lb.) | (g/lb.) | (mg/lb.) | ||||||
| $/lb. | ||||||||||
| Chicken | 500 | 4.2 | 17 | 0 | 30 | 180 | 0.85 | |||
| Fish | 480 | 3.1 | 85 | 0 | 5 | 90 | 3.35 | |||
| Ground beef | 840 | 0.25 | 82 | 0 | 75 | 350 | 2.45 | |||
| Dried beans | 590 | 3.2 | 10 | 30 | 3 | 0 | 0.85 | |||
| Lettuce | 40 | 0.4 | 6 | 0 | 0 | 0 | 0.7 | |||
| Potatoes | 450 | 2.25 | 10 | 70 | 0 | 0 | 0.45 | |||
| Milk (2%) | 220 | 0.2 | 16 | 22 | 10 | 20 | 0.82 | |||
| Constraints | >= | >= | >= | >= | >= | <= | ||||
| 1300 | 4 | 30 | 60 | 15 | 35 | |||||
| <= | <= | |||||||||
| 2100 | 55 | |||||||||
| (a) | Objective | Minimize Cost ($) | ||||||||
| (b) | if a serving of each of the the food items (other than milk) was limited to no more than a half pound, what effect would this have on the solution? | |||||||||
| Decision Variables | Chicken | <= | 0.5 | |||||||
| Fish | <= | 0.5 | ||||||||
| Ground beef | <= | 0.5 | ||||||||
| Dried beans | <= | 0.5 | ||||||||
| Lettuce | <= | 0.5 | ||||||||
| Potatoes | <= | 0.5 | ||||||||
| Milk (2%) | ||||||||||
| Objective | Minimize Cost ($) | |||||||||
| Answer: | No feasible solution found |
P4
| Jefferson County Regional HospitalScheduling | |||||||
| Let Xi = number of nurses that begin their 8 hour shift in period I (I = 1,2,3,4, …., 12) | |||||||
| period 1 | 12:00AM -- 2:00Am | ||||||
| period 2 | 2:00AM -- 4:00 AM etc | ||||||
| # of Nurses | Minimum # of | ||||||
| DV | Period | working | Nurses | ||||
| x1 | 1 | >= | 30 | ||||
| x2 | 2 | >= | 20 | ||||
| x3 | 3 | >= | 40 | ||||
| x4 | 4 | >= | 50 | ||||
| x5 | 5 | >= | 60 | ||||
| x6 | 6 | >= | 80 | ||||
| x7 | 7 | >= | 80 | ||||
| x8 | 8 | >= | 70 | ||||
| x9 | 9 | >= | 70 | ||||
| x10 | 10 | >= | 60 | ||||
| x11 | 11 | >= | 50 | ||||
| x12 | 12 | >= | 50 | ||||
| Objective Function |
P5
| Videotechnics Company (Multi Production and Inventory) | |||||||||
| Let Ri = Regular production in month I, where I = 1,2,3,4,5 | Cost for recorders produced during regular working hours is $10 | ||||||||
| Oi = Overtime production in month I, where I = 1,2,3,4,5 | Cost for recorders produced during regular working hours is $15 | ||||||||
| I_i = Inventory at end of month I, where I = 1,2,3,4 | |||||||||
| R1 | <= | 2000 | O1 | <= | 600 | I_1 | |||
| R2 | <= | 2000 | O2 | <= | 600 | I_2 | |||
| R3 | <= | 2000 | O3 | <= | 600 | I_3 | |||
| R4 | <= | 2000 | O4 | <= | 600 | I_4 | |||
| R5 | <= | 2000 | O5 | <= | 600 | ||||
| Month | |||||||||
| 1 | = | 1200 | |||||||
| 2 | = | 2100 | |||||||
| 3 | = | 2400 | |||||||
| 4 | = | 3000 | |||||||
| 5 | = | 4000 | |||||||
| Objective function |
