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

What do you mean by linear programming problem, Q1. a. What do you mean by ...

Q1. a. What do you mean by linear programming problem? Explain the steps involved in linear programming problem formulation? b. A paper mill produces two grades of paper viz., X

Usefulness of correlation - correlation regression analysis, Usefulness of ...

Usefulness of Correlation 1.Correlation is very useful to economists to study the relationship between variables like price and quantity demanded. To businessmen it

Mb0048, A paper mill produces two grades of paper viz., X and Y. Because of...

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

Scope, explain the significant and scope of operation research in scientifi...

explain the significant and scope of operation research in scientific management

LPP, A paper mill produces two grades of paper viz. X and Y. Because of raw...

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 in

Or, meaning,significance of operations research in bussiness management?

meaning,significance of operations research in bussiness management?

Anthology or book with articles or works by many authors , Anthology or Bo...

Anthology or Book with Articles or Works by Many Authors The name of the person compiling the book will be given followed by the word editor. For more than one edit

Short question, write down any two assumption of L.P

write down any two assumption of L.P

Assumption for students test , Assumption for students Test a.The p...

Assumption for students Test a.The parent population from which the samples is drawn in normal. b.The sample observations are random i ,e the given sample is drawn

Analyse the average number and mean number, Consider the closed network of ...

Consider the closed network of the following figure. The number at the arrows give the transition probabilities for a customer leaving the queue to route to a subsequent queue. Eve

Write Your Message!

Name

Email id

Message

Verfication Code

User Account

All Pages