Find the maximum and minimum values, Operation Research

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

 

 

 

 

 

 

19

63\13

Posted Date: 7/23/2012 4:12:11 AM | Location : United States







Related Discussions:- Find the maximum and minimum values, Assignment Help, Ask Question on Find the maximum and minimum values, Get Answer, Expert's Help, Find the maximum and minimum values Discussions

Write discussion on Find the maximum and minimum values
Your posts are moderated
Related Questions
Methods is a tool or a techniques used to collect data. It is procedure for obtaining knowledge based on empirical observation and logical reasoning. Field Study Metho

what is operation research an management decision making

Question 1 Explain any five accessory industries Question 2 Explain the history of boots and shoes Question 3 Write short notes on following- Types of Gujarati emb

The Omega company, Brisbane, produces potato chips, corn, cheese twists, and popcorn. These products are made in Brisbane and then shipped to company warehouses and distribution ce

Solve the following Linear Programming Problem using Simple method. Maximize Z= 3x1 + 2X2

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

One Sample Tests The one sample test is  applied  to a situation where  only a single sample ( one  sample) is taken from  a population in this test the researcher may  be tak

You are a manager at a medium sized manufacturing operation that sells a customized product directly to the consumers and the data pattern is linear but it can have the occasion ra

b. 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

Mode  of Presentation A strategy  needs to be  chalked out for  a satisfactory  rendering of the  topic. The  man oeuvres are going  t vary  with a  change in the  manner  of