Linear Programming Resource

Contents available at below site nicely explain Linear Programming, graphical method and Simplex method. You may also like to navigate through other pages of the site.

 

http://www.me.utexas.edu/~jensen/ORMM/methods/unit/linear/index.html

Linear Programming- Graphical Method- Test question

A Carpenter manufactures tables and chairs. He has all the resources in abundance except wood and nails. The profitability and resource requirements for the two products are given in following table. The availability of resources per day is also given. How many tables and chairs he should manufacture daily so that his profit is maximized? Formulate the linear programme and solve that using graphical method.

 

	Table	Chair
Profit/unit->	20$	30$	Availability/day v
Wood/unit in kg.	40	30	1200
Nails/unit in number	25	40	1000

 

If the profit/unit on table increases and rest of the data remains same, find the increased value of profit/unit on table so that the optimum product mix doesn’t change.

Evaluation of QT2 (2011-13)

Unannounced Class tests: 20 marks. Best 2 out of 4 tests of 10 marks each.

 

Announced Class test: 10 marks. One test of 10 marks.

 

Class Performance: 20 marks. Your roll number will be noted during the class if you ask good question. Depending on the number of good questions asked by you in the class, your marks in this part will be decided as per below table.

 

Number of times your roll number is noted	Marks
7 or more	19 or 20
6	17 or 18
5	15 or 16
4	13 or 14
3	11 or 12
Less than 3	Come for viva

 

Your response to questions asked in the class will be considered in awarding one of the two marks as per the above table.

 

Group work/ Presentation: 20 marks

 

End term examination: 30 marks.

Project Management - An Exercise

There is a race ground with 15 racetracks. A team has to complete all the 15 tracks to complete the race. There are few tracks that can be done in the beginning. However for other tracks it is necessary to finish some other tracks and press the finish button then only the entrance gate opens. You can form your team of as many members as you want to finish the race in best possible time. The time required to complete a track and the tracks that needs to be completed before starting this track are given in the below table.

 

 

Track	Time required in minutes	Tracks to be completed before starting this track
A	45	None
B	25	None
C	15	None
D	20	A
E	30	B
F	30	C
G	15	D
H	40	E, F
I	40	C
J	35	G, H
K	10	H
L	15	I
M	35	I
N	20	K, L
O	30	M

 

Time required in changing the track or any other related activities are already included in the time given above. So, there is no need to consider any other time element.

 

1. Find the minimum time in which the race can be completed and for that what should be your team size. A team member can cover more than one track one after other.

 

2. Just before the start of the race, your team members inform you that they will be late by about 4 minutes. You can run any of the A, B, or C tracks. Which one you will run? Will it impact your team overall performance in the race?

 

3. You are given two cycles that can be used on any two tracks in the race. Use of cycle on a track reduces the time requirement for that track by 40%. In which two tracks would you use them to get the best race time?

 

4. Let there be another track P introduced in the race that needs to be completed before N can be started. However to start P it is necessary to finish track C. Time required to complete the track P is 50 minutes. What would be the impact of introduction of this track on your race completion time with and without cycle?

 

 

 

Linear Programming - What to expect

If you have any objective like maximize profit or minimize loss or maximize customer satisfaction or minimize some claim function or something like this, you can obviously maximize the objective to infiniy or minimize to zero or minus infinity as the case may be. But it is ususally not done. Because there are constraints. An organization manufacturing cars donot produce infinite number of cars because it may not have that much demand or may be it is constrained by capacity etc.

If objective and constraints can be expressed in the form of linear expressions, the problem can be programmed as a linear programme and solved.

Everyone here will be able to do this. But we will try to go ahead. You should try to get important insight using Linear Programme into decision situations where if you are given additional fund, you should be able to decide about its use to get best result.