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

 

 

 

 

 

 

19

63\13


Related Discussions:- Find the maximum and minimum values

Uses of range - measure of dispersion, Uses of Range a.Range is suitab...

Uses of Range a.Range is suitable  measure  of dispersion  when the  data are too  scattered to justify the  computation of a more precise  measure of dispersion. b.In rece

A paper mill produces two grades of paper viz., A paper mill produces two g...

A paper mill produces two grades of paper viz., X & Y. Because of raw material restrictions, it cannot produce more 400 tons of grade X paper & 300 tons of grade Y paper in a week.

Optimal assigment, #quesSix Operators are to be assigned to five jobs with ...

#quesSix Operators are to be assigned to five jobs with the cost of assignment in Rs. given in the matrix below. Determine the optimal assignment. Which operator will have no assig

Inherent limitation concerning mathematical expressions, Operation reac Inv...

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

Paired sample sign test - hypothesis testing , Paired sample  sign Test ...

Paired sample  sign Test Paired samples  sign test is applied  to a situation where two sample  are taken from  two population which  have continuous symmetrical distributi

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd