Find the maximum and minimum values, Operation Research

Assignment Help:

Problems based on solution of a given LPP when it has multiple optimal solution:

1. Find the maximum and minimum values of 5x+2y, subject to the constraints

-2x-3y ≤ -6

x-2y ≤ 2

6x + 4y ≤ 24

-3x + 2y ≤ 3

X, y ≥ 0

script

solution

1. Let z is equal to

Let us draw the lines - 2x-3y = -6, X - 2y =2

6x+ 4y = 24

2. using suitable points on the graph.

3. Now shade the region of intersection of the 3 lines.

4. The shaded region ABCD represents the region of feasible region

5. The Vertices of feasible region are

6. Now let us find the maximum and minimum values by using these points

7. For the corner point A(18/7,2/7)

8. For the corner point B(7/2,3/4)

9. For the corner point C(3/2,15/4)

10. For the corner point D(3/13,24/13)

11. We find the maximum value occurs at vertex B, minimum value at vertex D

Maximum value

Minimum value

Z = 5x + 2y

2x + 3y = 6

X - 2y =2

6x+ 4y = 24

- 3x + 2y = 3

A ( 18\7,2\7) B(7\2,3\4) C(3\2,15\4) D(3\13,24\13)

5(18/7)+2(2/7)= 94/7

5(7/2)+2(3/4)=76/4

5(3/2)+2(15/4)=60/4

5(3/13)+2(24/13)=63/13

63\13

Related Discussions:- Find the maximum and minimum values

Features of Operations Research?, What are the features of Operations Resea...

What are the features of Operations Research?

Linear programming, A paper mill produces two grades of paper viz., X and Y...

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

Bibliography format - report writing presentation , Bibliography Format ...

Bibliography Format a. Introduction : Bibliographies tell readers where they can locate information about a topic. It is a list of sources of information for a repo

Graphical solution procedure, Graphical Solution Procedure sample assignmen...

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

Operation research model, methods for solving operation research models

methods for solving operation research models

Linear programing, A paper mill produces two grades of paper viz., X and Y....

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

Set of pareto optimal policies, Problem: A policy maker is considering seve...

Problem: A policy maker is considering several policy options that lead to different utility levels of different individuals a) Which Policy is would be optimal according t

Purchasing power of customers, This is determined by disposable personal ...

This is determined by disposable personal income( personal income minus direct taxes and other deductions ). Some people suggest the use of discretionary income in place of

Describe states-transitions and transition rate, Customers arrive to a supe...

Customers arrive to a super market according to a Poisson process with intensity V = ½ per minute. The supermarket has two counters, that use a common queue. Counter 1 is always o

Simple line graphs , Simple Line Graphs a. Simple Histogram A simpl...

Simple Line Graphs a. Simple Histogram A simple histogram is a techniques used plotting a time series on the graph paper. The data are arranged according to the time

Write Your Message!

Name

Email id

Message

Verfication Code

User Account

All Pages