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  • Please solve RD Sharma class 12 chapter Linear Programming exercise 29.2 question 17 maths textbook solution

Please solve RD Sharma class 12 chapter Linear Programming exercise 29.2 question 17 maths textbook solution

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Answer: the maximum value of 2 is infinity

Hint: Plot the points on the graph

Given:z =2x +3y
solution:First, we shall convert the given equation into equations, we obtain the following equations the following equationsx+y =1,10x +y =5, x+10y=1,x=0and y=0.Region represented by x+y\geq 1 The

line x+y=1,meets the coordinates axes at A(0,-1) and B(0,1) respectively .By joining these points we obtain the line x+y=1,clearly (0,0) does not satisfy the equation x+y\geq 1.So the region in x y plane which does not contain the origin represents the solution set of the equation x+y\geq 1 region represented by 10x+y\geq 5 the line 10x+y=5  meets the coordinates at  C\left(\frac{1}{2^{\prime}} 0\right) \text { and } D(0,5) respectively .By joining these

points we obtain the line 10x +y\geq 5, clearly (0,0)does not satisfy the equation 10x +y\geq 5,

.so the region which does not contain the origin represents the solution set of the in equation 10x +y\geq 5,
Region represented by \lambda+10 y \geq 1 : The line \lambda+=10 y=1 meets the coordinates axes at A(1,0) \text { and } F\left(0, \frac{1}{10}\right)  respectively. By joining these points we obtain the line \lambda+=10 y=1 , clearly (0,0) does not satisfy the  equation \lambda+10 y \geq 1
Region represented by x \geq 0 \text { and } y \geq 0: since, every point of the first quadrant satisfies these equation.so the first quadrant is the region represented by the equation x \geq 0 \text { and } y \geq 0

The feasible region determined by the system of constraints x+y \geq 1,10 x+y \geq 5, x \geq 0 \text { and } y \geq 0 are as follows

The feasible region is unbounded.Therefore,the maximum value is infinity i.e the solution is unbounded

 

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