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  • Provide solution for RD Sharma maths class 12 chapter Linear Programming exercise 29.2 question 26

Provide solution for RD Sharma maths class 12 chapter Linear Programming exercise 29.2 question 26

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Answer: the maximum value if ? is 10

Hint: plot the points on the graph

Given: maximize: Z=2 x+5 y

Solution: the given constraints are

                \begin{aligned} &2 x+4 y \leq 8----(1) x+y \leq 4--(3) \\ &3 x+y \leq 6----(2) x \geq 0, y \geq 0 \end{aligned}

We need to maximize the objective function Z=2 x+5 y  . Converting the equations into equations, we obtain the lines 2 x+4 y=8,3 x+y=6, x+y=4, x=0, y=0

These lines are drawn and the feasible region of the LPP is shaded.

The coordinates of the corner points of the feasible regions are

                O(0,0), A(0,2), B(1.6,1.2), C(2,0)

The values of the objects function at the points are given in the following table;

\begin{array}{|l|l|} \hline \text { Points } & \text { Values of the objective function } z=2 x+5 y \\ \hline O(0,0) & 2(0)+5(0)=0 \\ A(0,2) & 2(0)+5(2)=10 \\ B(1.6,1.2) & 2(1.6)+5(1.2)=9.2 \\ C(2,0) & 2(2)+5(0)=4 \\ \hline \end{array}

Out of these values of Z, the maximum value of Z is 10

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