MAT 540
hhocha
hw8_answer_sheet_2015.xlsxP1
| Grafton Metalworks Company | |||||||||
| Ore | Metal (%) | Impurities | Cost/Ton | ||||||
| A | B | C | D | ||||||
| 1 | 0.19 | 0.15 | 0.12 | 0.14 | 0.4 | 27 | |||
| 2 | 0.43 | 0.1 | 0.25 | 0.07 | 0.15 | 25 | |||
| 3 | 0.17 | 0 | 0 | 0.53 | 0.3 | 32 | |||
| 4 | 0.2 | 0.12 | 0 | 0.18 | 0.5 | 22 | |||
| 5 | 0 | 0.24 | 0.1 | 0.31 | 0.35 | 20 | |||
| 6 | 0.12 | 0.18 | 0.16 | 0.25 | 0.29 | 24 | |||
| Composition constraints | A | >= | 0.21 | ||||||
| B | <= | 0.12 | |||||||
| C | <= | 0.07 | |||||||
| D | >= | 0.3 | |||||||
| D | <= | 0.65 | |||||||
| Impurity constraint | Metal | 0.00 | = | 1 | Note: Purities = 1 - impurities | ||||
| Note: puroty contents of ores must be = 1 | |||||||||
| Ore | |||||||||
| Decision variables | |||||||||
| 1 | |||||||||
| 2 | |||||||||
| 3 | |||||||||
| 4 | |||||||||
| 5 | |||||||||
| 6 | |||||||||
| Objective function | Minimize Cost ($) |
P2
| congressman’s district | ||||||
| Program | Votes/ Dollar | |||||
| Job training | 0.02 | |||||
| Parks | 0.09 | |||||
| Sanitation | 0.06 | |||||
| Mobile library | 0.04 | |||||
| Comments | ||||||
| Constraints | <= | 1600000 | Job training | |||
| <= | 1600000 | Parks | ||||
| <= | 1600000 | Sanitation | ||||
| <= | 1600000 | Mobile library | ||||
| <= | Parks <= Sanitation + Mobile Library | |||||
| >= | Job training >= Sanitation | |||||
| spending | = | 4000000 | 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.) | ||||||
| $/lb. | ||||||||||
| Chicken | 520 | 4.4 | 17 | 0 | 30 | 180 | 0.8 | |||
| Fish | 500 | 3.3 | 85 | 0 | 5 | 90 | 3.7 | |||
| Ground beef | 860 | 0.3 | 82 | 0 | 75 | 350 | 2.3 | |||
| Dried beans | 600 | 3.4 | 10 | 30 | 3 | 0 | 0.9 | |||
| Lettuce | 50 | 0.5 | 6 | 0 | 0 | 0 | 0.75 | |||
| Potatoes | 460 | 2.2 | 10 | 70 | 0 | 0 | 0.4 | |||
| Milk (2%) | 240 | 0.2 | 16 | 22 | 10 | 20 | 0.83 | |||
| Constraints | >= | >= | >= | >= | >= | <= | ||||
| 1500 | 5 | 30 | 40 | 20 | 30 | |||||
| <= | <= | |||||||||
| 2000 | 60 | |||||||||
| Decision Variables | Chicken | <= | 0.5 | |||||||
| Fish | <= | 0.5 | ||||||||
| Ground beef | <= | 0.5 | ||||||||
| Dried beans | <= | 0.5 | ||||||||
| Lettuce | <= | 0.5 | ||||||||
| Potatoes | <= | 0.5 | ||||||||
| Milk (2%) | ||||||||||
| Objective | Minimize Cost ($) | |||||||||
| a. If a serving of each of the food items (other than milk) was limited to no more than a half pound, what effect would this have on the solution? | ||||||||||
| Answer: |
P4
| Cabin Creek Coal (CCC) | Note: No quality constraints | ||||||||
| Cost (Processing & Mining) | Mine 1 | Mine 2 | Mine 3 | ||||||
| $ | 62 | 67 | 75 | ||||||
| Plant | |||||||||
| Mine | 1 | 2 | 3 | 4 | Constraints | Mine Capacity (tons) | |||
| 1 | $7 | $9 | $10 | $12 | <= | 220 | |||
| 2 | 9 | 7 | 8 | 12 | <= | 170 | |||
| 3 | 11 | 14 | 5 | 7 | <= | 280 | |||
| Constraints | |||||||||
| = | = | = | = | ||||||
| Demand (tons) | 110 | 160 | 90 | 180 | |||||
| DV | Mine to Plant | Please ignore "Quality constraints" in the problem | |||||||
| x11 | No feasible solution if quality constraints imposed | ||||||||
| x12 | |||||||||
| x13 | |||||||||
| x14 | |||||||||
| x21 | |||||||||
| x22 | |||||||||
| x23 | |||||||||
| x24 | |||||||||
| x31 | |||||||||
| x32 | |||||||||
| x33 | |||||||||
| x34 | |||||||||
| Objective Function | Minimize Cost | ||||||||
P5
| Joe Henderson Assignments | |||||||||||
| 1, 2 | Operator | Drill Press (min) | Lathe (min) | Grinder (min) | |||||||
| 1 | 23 | 18 | 35 | ||||||||
| 2 | 41 | 30 | 28 | ||||||||
| 3 | 25 | 36 | 18 | ||||||||
| DV | Operator | Drill Press | Lathe | Grinder | Operator Constraints | Assignment | |||||
| 1 | 1 | 0 | 0 | = | 1 | ||||||
| 2 | 0 | 1 | 0 | = | 1 | ||||||
| 3 | 0 | 0 | 1 | = | 1 | ||||||
| Machine Constraints | |||||||||||
| = | = | = | Note: Constraints | = | Integer | ||||||
| 1 | 1 | 1 | |||||||||
| Objective | Minimize Time | ||||||||||
| 3 | Operator | Drill Press (min) | Lathe (min) | Grinder (min) | |||||||
| 1 | 23 | 18 | 35 | ||||||||
| 2 | 41 | 30 | 28 | ||||||||
| 3 | 25 | 36 | 18 | ||||||||
| 4 | 20 | 20 | 20 | ||||||||
| DV | Operator | Drill Press | Lathe | Grinder | Operator Constraints | Assignment | |||||
| 1 | 0 | 1 | 0 | <= | 1 | ||||||
| 2 | 0 | 0 | 0 | <= | 1 | ||||||
| 3 | 0 | 0 | 1 | <= | 1 | ||||||
| 4 | 1 | 0 | 0 | <= | 1 | ||||||
| Machine Constraints | |||||||||||
| = | = | = | Note: Constraints | = | Integer | ||||||
| 1 | 1 | 1 | |||||||||
| Objective | Minimize Time | ||||||||||
| Answer | Should Joe hire Fred's wihe? | (Yes / No) | Note: Minimize time |
P6
| Cash and Carry Building Supply Company | |||||||||||
| The company determines how to cut the 25-foot boards to meet the order requirements and minimize the number of standard-length boards used | |||||||||||
| Length | Order (quantity) | Note: There are 6 possible patterns you can cut the board (shown in #1 through #6) | |||||||||
| 7 ft. | 700 | Example #1 pattern | cut the 25-foot board into 3 7-foot board (waste 25-3*7 = 4 feet) | ||||||||
| 9 ft. | 1,200 | Example #4 pattern | cut 25-foot board into 1 7-foot, 2 9-foot boards (waste = 25-(1*7+2*9) = 0) | ||||||||
| 10 ft. | 300 | ||||||||||
| What are possible patterns the standard board can be cut? | |||||||||||
| Possible cut patterns | |||||||||||
| #1 | #2 | #3 | #4 | #5 | #6 | Constraints | Order (quantity) | ||||
| 7 | 3 | 2 | 2 | 1 | 0 | 0 | = | 700 | |||
| 9 | 0 | 0 | 1 | 2 | 1 | 0 | = | 1,200 | |||
| 10 | 0 | 1 | 0 | 0 | 1 | 2 | = | 300 | |||
| Total length | 21 | 24 | 23 | 25 | 19 | 20 | |||||
| <= | <= | <= | <= | <= | <= | ||||||
| 25 | 25 | 25 | 25 | 25 | 25 | ||||||
| Decision Variables | |||||||||||
| Objective | Minimize standard boards | ||||||||||
| What are possible patterns the standard board can be cut? | |||||||||||
| Possible cut patterns | |||||||||||
| #1 | #2 | #3 | #4 | #5 | #6 | Constraints | Order (quantity) | ||||
| 7 | 3 | 2 | 2 | 1 | 0 | 0 | >= | 700 | |||
| 9 | 0 | 0 | 1 | 2 | 1 | 0 | >= | 1,200 | |||
| 10 | 0 | 1 | 0 | 0 | 1 | 2 | >= | 300 | |||
| Total length | 21 | 24 | 23 | 25 | 19 | 20 | |||||
| Trim Loss | 4 | 1 | 2 | 0 | 6 | 5 | |||||
| Decision Variables | |||||||||||
| Objective | Minimize standard boards trim loss | Minimize trim loss |
