Graphical solution procedure, Operation Research

Graphical Solution Procedure sample assignment and solved questions, free examples and solved homework samples for Graphical Solution Procedure in operation research.

Question: Max Z = 80x1 + 55x2

Subject to

4x1+ 2x2 ≤ 40

            2x1 + 4x2 ≤ 32

 x1 ≥ 0 , x2 ≥ 0

 

Answer

The first constraint 4x1+ 2 x2 ≤ 40, can be written in a form of equation

4x1+ 2 x2 = 40

Place x1 =0, then x2 = 20

Place x2 =0, then x1 = 10

Therefore, the coordinates are (0, 20) and (10, 0)

 

The second constraint 2x1 + 4x2 ≤ 32, can be written in a form of equation

2x1 + 4x2 =32

Place x1 =0, then x2 = 8

Place x2 =0, then x1 = 16

Therefore, the coordinates are (0, 8) and (16, 0)

 

The graphical presentation is

84_Graphical_Solution_Procedure.png

 

The corner positions of feasible region are A, B and C. Thus the coordinates for the corner points are

A (0, 8)

B (8, 4) (Crack the two equations 4x1+ 2 x2 = 40 and 2x1 + 4x2 =32 to obtain the coordinates)

C (10, 0)

 

We are given that Max Z = 80x1 + 55x2

At A (0, 8)

Z = 80(0) + 55(8) = 440

 

At B (8, 4)

Z = 80(8) + 55(4) = 860

 

At C (10, 0)

Z = 80(10) + 55(0) = 800

 

The maximum value is achieved at the point B. Thus Max Z = 860 and x1 = 8, x2 = 4

Posted Date: 7/4/2012 3:36:51 AM | Location : United States







Related Discussions:- Graphical solution procedure, Assignment Help, Ask Question on Graphical solution procedure, Get Answer, Expert's Help, Graphical solution procedure Discussions

Write discussion on Graphical solution procedure
Your posts are moderated
Related Questions
Information on Research Done Information on Doctoral research work already done  is available from  the followings  sources: a. Bibliography of Doctoral  Dissertations Acce

The town of Silverton, Colorado, has three gasoline stations, Shell, Exxon, and Arco. Customer selection of service stations can be modeled as a Markov process, with the following

Operation reac Involves the use of mathematical models, equations and similar other mathematical expressions. Assumptions are always incorporated in the derivation of an equa

Show simple vapour compression Refrigeration cycle with showing all the devices and also draw T-sand P-R diagram and illustrate it also. A Bell-Coleman cycle works between 1 bar

Select one of the topics listed 1-6 below and outline a programme of quantitative research for its investigation.  The assignment  should cover issues of sample design, instrumen

management wants to know how many supervisors should be hired, and what could be the optimum workload distribution to be applied, given a number of constraints


A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y paper i

3. A paper mill produces two grades of paper viz., X and Y. Because of raw material restrictions, it cannot produce more than 400 tons of grade X paper and 300 tons of grade Y pape

Need Proposals are written for various reasons. They are prepared for different reasons which vary to the extent of details expected, but like research reports, the proposal a