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  • Please solve RD Sharma class 12 chapter Linear Programming exercise 29.2 question 9 maths textbook solution

Please solve RD Sharma class 12 chapter Linear Programming exercise 29.2 question 9 maths textbook solution

Answers (1)

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Answer:

The optimal value of z is 246000.

Hint:

Plot the points on the graph.

Given:

z=7x+10y

Solution:

We have to maximize z=7x+10y

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

x+y=30000,y=12000, x=6000, x=y, x=0 and y=0

Region presented by x+y\leq 30000 . The linex+y=30000 meets the coordinate axes at A(30000,0 ) and B(0,30000) respectively. By joining these points are obtain the line x+y=30000. Clearly,(0,0) satisfies the equation x+y\leq 30000 . The line y=12000  is the line that passes through C(0,12000)  and parallel to x-axis.

Region presented by x\geq y . the line passes through the origin. The points to the right of the line x=y  satisfies the equation x\geq y . like by the taking the points( -12000,6000) Hence ,6000>-12000  which implies y>x. hence, the points to the left of the line x=y  will not satisfy the given equation x\geq y. region represented 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 equation x\geq 0 and y\geq 0.

The feasible region determined by the system of constraints,
x+y\leq 30000, y\leq 12000, x\geq 6000, x\geq y, x\geq 0 and y\geq 0 are as follows

The corner points of the feasible region are

F(18000,12000) and E(12000,12000)

The value of z at these corner points are as follows

\begin{array}{|c|c|} \hline \text { Corner Points } & z=7 x+10 y \\ \hline D(6000,0) & 7 \times 0+10 \times 0=42000 \\ \hline A(3000,0) & 7 \times 3000+10 \times 0=21000 \\ \hline F(18000,12000) & 7 \times 18000+10 \times 12000=246000 \\ \hline E(12000,12000) & 7 \times 12000+10 \times 12000=204000 \\ \hline \end{array}

Therefore, the maximum value of objective function z is 246000 at the point F(18000,12000) The means at x=18000 and y=12000. Thus, the optimal of z is 246000.

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