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  • Please solve RD Sharma class 12 chapter Linear Programming exercise 29.2 question 21 maths textbook solution

Please solve RD Sharma class 12 chapter Linear Programming exercise 29.2 question 21 maths textbook solution

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Answer: maximum value will be infinity (\infty)

Hint: plot the points on the graph.

Given: z=3x+3y

Solution: first we will convert the gives equation into equations, we obtain the following equations; \lambda-y=1, \lambda+y=3, \lambda=0, y=0

Region represented by  \lambda-y \leq 1 . The line  \lambda-y=1  meets the coordinates are at A(1, 0) and B(0, 1) respectively. By joining these points we obtain the line  \lambda-y=1  . Clearly (0, 0) satisfies the equation \lambda+y \leq 8 . So the region in xy plane which contain the origin represents the solution set of the equation \lambda-y \leq 1

Region represented by \lambda+y \geq 3 . The line \lambda+y=3   meets coordinates axes at C(3,0) and O (0, 3) respectively. by joining these points we obtain the line \lambda+y=3

Clearly (0, 0) satisfies the equation \lambda+y \geq 3 \text {. } . So the region in my plane which does not contain the origin in xy plane which does not contain the origin represents the solution set of the equation \lambda+y \geq 3 .

Region represented by \lambda \geq 0 \text { and } y \geq 0 . since every point s the first quadrant satisfies these equations. So the first quadrant is the region represented by the equations \lambda \geq 0 \text { and } y \geq 0 .

The feasible region determined by the system of constraints \lambda-y=1, \lambda+y=3, \lambda=0, y=0

                The feasible region is unbounded . we would obtain the maximum value at infinity, therefore maximum value will be infinity i.e. the solution is unbounded.

 

 

 

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