VICTORIA UNIVERSITY Case Study 2 (30%) Due Week 11 BEO 6501 Quantitative Analysis Semester 2,… 1 answer below »

VICTORIA UNIVERSITYCase Study 2 (30%)Due Week 11

BEO 6501 Quantitative AnalysisSemester 2, 2014

Instructions

Thispartrequires students to solveusinga linear-programming problem/an integer-programming problem/goalprogrammingproblem.

There is an objective function that has to be maximised or minimised, subject to a set of constraints. Students should clearly define the decision variables, defineand explain the objective function and defineand explain each of the constraints. In addition, the solutions must be clearly and fully explained.

In order that students and groups tackle unique problems, students are asked to consider their student id numbers. All ids are made up of seven digits of the form 3664255.The particular digits in yourand your partnerids will appear at various places below. If, for example,your id is3664255 and you see a reference toA, B, C for you this means6,6, 4. In addition, 2C means 24.Then, if, for example, your partner id is 4885255 and you see a reference to D, E, F, this means8, 8, 5. Then, 2E means 28.If you work by yourself, A-F are your 6 last digit IDs.

For these parts, the report needs to address the followings.

The report should tell a story.

All variables should be clearly defined.

For each problem, define and briefly explain the objective function specified as an equation. For example, P = 3X1 + 5X2.

For each problem, define and briefly explain all of the constraints specified as equations or inequalities. For example, 4X1 + 13X2? 100.

Present the solutions as tables.

Solver answer reports should not be in the main text of the report. If you want to include them, place them in an appendix.

Part A: Healthy Foods Incorporated (11)

Healthy Foods Incorporated is selecting the ingredients for a batch of Peanut Bars, Coconut Whirls and Fruit Logs. The following table shows the ingredients that are available and the costs per kilogram.

Ingredient

Cost ($/Kgm)

Available quantity (Kgm)

Milk chocolate

1.2A

1,500

Sugar

0.3B

300

Peanuts

1.8C

600

Coconut

0.9D

400

Milk solids

0.4E

200

Dried fruit

2.2F

400

Healthy Foods wants to determine the minimum cost mixture for an order of 1,000 kilograms of Peanut Bars, 800 kilograms of Coconut Whirls and 700 kilograms of Fruit Logs.

In Peanut Bars:

the weight of chocolate must be at least 50 percent of the total weight;

the weight of sugar should be no more than 10 percent of the total weight;

the weight of peanuts must be at least 30 percent of the total weight;

there should be no coconut;

the weight milk solids must be no less than 10 percent and no more than 20 percent the total weight; and

there should be no dried fruit.

In Coconut Whirls:

the weight of chocolate must be at least 40 percent the total weight;

the weight of sugar should be no more than 10 percent of the total weight;

there should be no peanuts;

the weight coconut must be at least 30 percent and no more than 40 percent of the total weight;

the weight milk solids must be no less than 10 percent and no more than 20 percent the total weight; and

there should be no dried fruit.

In Fruit Logs:

the weight of chocolate must be at least 50 percent of the total weight;

the weight of sugar should be no more than 10 percent of the total weight;

the weight of peanuts must be at least 10 percent and no more than 20 percent of the total weight;

the weight coconut must be at least 10 percent and no more than 20 percent of the total weight;

there should be no milk solids; and

the weight dried fruit must be at least 20 percent of the total weight.

Formulate the linear-programming problem. Solve it usingExcel Solver. Produce a report concerning the model and the results, including the values of the slack and surplus variables.

How would the solution change if the price of milk chocolate was 50 percent less than its original value?

Part B: Rocket Cargo Incorporated (11)

Rocket Cargo Incorporated takes delivery 630 litre refrigerators at three warehouses supplied from five factories. The following table shows the transport costs in dollars per unit shipped between the factories and the warehouses. It also shows for the next planning period the stocks at each factory and the capacity to handle the product at each warehouse.

Warehouse

Factory

W1

W2

W3

Stock

F1

1A

2E

3E

250

F2

1B

2F

3F

300

F3

2C

3F

3A

200

F4

1D

3A

3B

350

F5

2E

2B

2D

150

Capacity

300

400

500

Rocket delivers refrigerators from the three warehouses to seven retail businesses. The following table shows the transport costs in dollars per unit shipped between the warehouses and the retail businesses. It also shows the demand at each retail business.

Retail Business

Warehouse

R1

R2

R3

R4

R5

R6

R7

W1

1A

2E

5A

4A

1A

2B

2B

W2

1B

2F

2B

3B

2B

1A

1A

W3

2C

2A

1C

4D

2E

2C

2C

Demand

190

180

220

170

210

240

180

Formulate this transhipment problem as a cost minimisation integer-programming problem. Solve it usingExcel Solver. What is the optimal transhipment plan? Which if any of the factories will have stock left over, which if any of the warehouses will have unused capacity and which if any of the retail businesses will be undersupplied?

How will the solution change if there is penalty of $25 per unit short at retail business R4?

Part C:The Farmer’s American Bank of Leesburg (7)

The Farmer’s American Bank of Leesburg is planning to install a new computerised accounts system. Bank management has determined the activities required to complete the project, the precedence relationships of the activities, and activity time estimates, as shown in the following table:

Determine the expected projectcompletion time and variance and determine the probability that the project will be completed in 40 weeks or less.

The manager plans to crash the project. The data is below.

Activity

Activity Time (weeks)

Activity Cost

Normal

Crash

Normal

Crash

a

9

7

4800

6300

b

11

9

9100

15500

c

7

5

3000

4000

d

10

8

3600

5000

e

1

1

0

0

f

5

3

1500

2000

g

6

5

1800

2000

h

3

3

0

0

i

1

1

0

0

j

2

2

0

0

k

8

6

5000

7000

Thenormal activity times are considered to be deterministic and not probabilistic. Using the computer, crash the network to 26 weeks. Indicate how much it would cosy the bank and then indicate the critical path.

General Matters

This assignment is worth 30% of the total mark for the subject. This is a group assignment, which must be submitted in pairs of two students. Each member of the group will receive the same mark. However, students who do not cooperate or contribute equally towards the work of the group may be penalised and /or asked to make an individual submission for the whole assignments.

You are encouraged to submit your assignment using a word processor to improve your presentation. You will lose marks for bad presentation. English expression will also be counted within the marking scale. Report presentation is 1 mark.

Use A4 size paper and fasten assignment on the left-hand side. Do not use folder or plastic covers. Students must retain a copy of their assignment. Also remember plagiarism is a serious offence.

If you are in any doubt about any aspects of this case study, communicate with me at siti.nuryanah@vu.edu.au.

Due:End of week11.

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