Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Need solution for RD Sharma maths class 12 chapter Linear Programming exercise 29.2 question 15

Need solution for RD Sharma maths class 12 chapter Linear Programming exercise 29.2 question 15

Answers (1)

best_answer

Answer:

The optimal value of z is 55.

Hint:

Plot the points on the graph.

Given:

z=3x+5y

Solution:

First, we will convert the given in equations into equations, we obtain the following equations

x+2y=20, x+y=15, y=5, x=0 and y=0.

The line x+2y=20  meets the coordinate axes at A(20,0) and B(0,10)  respectively. By joining these points are obtain the line x+2y=20.

Clearly,( 0,0)  satisfies the equation x+2y\leq 20 . So, the region in xy-plane that contain the origin represents the solution set of the given equation.

The line  x+y=15  meets the coordinate axes at C(15,0) and D(0,15)  respectively. By joining these points are obtain the line x+y=15

Clearly, ( 0,0)  satisfies the equation  x+y\leq 15 . So, the region in xy-plane that contain the origin represents the solution set of the given equation.

Y=5 is the line passing through (0,5) parallel to the x-axis. The region below the line y=5 will satisfy the given equation.

Region presented by x\geq 0  and y\geq 0 . Since every point in the first quadrant satisfies these equations. So, the first quadrant is the region represented by the given equation.

The lines are drawn using a suitable scale.

The corner points of the feasible region are

0(0,0), C(15,0), E(10,5) \text { and } F(0,5)

The value of z at these corner points are as follows

\begin{array}{|c|c|} \hline \text { Corner Points } & z=3 x+5 y \\ \hline 0(0,0) & 3 \times 0+5 \times 0=0 \\ \hline C(15,0) & 3 \times 15+5 \times 0=45 \\ \hline E(10,5) & 3 \times 10+5 \times 5=55 \\ \hline F(0,5) & 3 \times 0+5 \times 5=25 \\ \hline \end{array}

We see that the maximum value of objective function z is 55  at the point E(10,5 )

Thus, the optimal of z is 55.

 

Posted by

infoexpert26

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Class 12 result verification 2024 application out at cbse.gov.in; last date, fees
anam-khan

CBSE results 2024 later for 102 students over fake certificates; board issues show cause notice
anam-khan

What after CBSE Class 12 results 2024? From CUET UG to JEE Advanced, all you need to know

Latest Question