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  • Provide solution for RD Sharma maths class 12 chapter Linear Programming exercise 29.2 question 10

Provide solution for RD Sharma maths class 12 chapter Linear Programming exercise 29.2 question 10

Answers (1)

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Answer:

The optimal value of z is 20.

Hint:

Plot the points on the graph.

Given:

z=2x+4y

Solution:

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

x+y=8,x+4y=12, x=3, and \; y=2

Region presented by  x+y\geq 8 . The line x+y=8  meets the coordinate axes at A(8,0) and B(0,8)   respectively. By joining these points are obtain the line  x+y=8 . Clearly,(0,0) does not satisfies the

equation x+y\geq 8 . So, the region in xy plane which does not contain the origin represents the solution set of the equation x+y\geq 8.

Region presented by x+4y\geq 12 . The line x+4y=12  meets the coordinate axes at C(12,0 ) and D(0,3) respectively. By joining these points are obtain the line x+4y=12. Clearly, (0,0)  satisfies the

equation x+4y\geq 12 . So, the region in xy plane which does not contain the origin represents the solution set of the equation x+4y\geq 12.

The line x=3 is the line that passes through the point (3,0) and is parallel to y-axis. x\geq 3 is the region to the right the line x=3.

The line y=2  is the line that passes through the point (0,12) and is parallel to x-axis yx\geq 2 is the region above the line y=2.

The value of z at these corner points are as follows

\begin{array}{|c|c|} \hline \text { Corner Points } & z=2 x+4 y \\ \hline E(3,5) & 2 \times 3+4 \times 5=26 \\ \hline F(6,2) & 2 \times 6+4 \times 2=20 \\ \hline \end{array}

Therefore, the maximum value of objective function z is 20 at the point F(6,2)

Hence,  x=6  and y=2  is the optimal solution of the given LPP.

Thus, the optimal of z is 20.

 

 

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