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Name: Provide solution for RD Sharma maths class 12 chapter Linear Programming exercise 29.2 question 14
Uploaded: Wed, 2021-09-08 14:59
Description: Provide solution for RD Sharma maths class 12 chapter Linear Programming exercise 29.2 question 14

Provide solution for RD Sharma maths class 12 chapter Linear Programming exercise 29.2 question 14

Answers (1)

Answer:

The optimal value of z is 4.

Hint:

Plot the points on the graph.

Given:

$z=x-5y+20$

Solution:

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

$x-y=0,-x+2y=2, x=3, y=4, x=0$ and $y=0.$

Region represented by $x-y\geq 0$ or $x\geq y$ . The line $x-y=0$ or $x=y$ passes.

Through origin. The region to the right of the line $x=y$ will satisfy the given equation. Lets check by taking an example like if we use take a point (4,3) to the right of the line $x=y$ . there $x\geq y$ . that means it does not satisfy the given equation.

Region represented by $-x+2y\geq 2$ . The line $-x+2y=2$ meets the coordinate axes at $A(-2,0)$ and $B(0,1)$ respectively. By joining these points are obtain the line $-x+2y=2$ .

Clearly, $(0,0)$ does not satisfies the equation $-x+2y\geq 2$ . So, the region in xy-plane which does not contain the origin represents the solution set of equation $-x+2y\geq 2$

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 of the line $x=3$

The line $y=4$ is the line that passes through the point (0,4) and is parallel to x-axis $y\leq 3$ is the region to the right of the line $y=4$

Region presented 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 the equation $x\geq 0$ and $y\geq 0$ .