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Name: Explain solution RD Sharma class 12 chapter Linear Programming exercise 29.2 question 12 maths
Uploaded: Wed, 2021-09-08 14:30
Description: Explain solution RD Sharma class 12 chapter Linear Programming exercise 29.2 question 12 maths

Explain solution RD Sharma class 12 chapter Linear Programming exercise 29.2 question 12 maths

Answers (1)

Answer:

The optimal value of z is 60 .

Hint:

Plot the points on the graph.

Given:

$z=30x+20y$

Solution:

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

$x+y=8, x+4y=12, x=0$ and $y=0$

Region presented by $x+y\leq 8$ . The line $x+y=8$ meets the coordinate axes at $A(8,0)$ and $B(0,8)$ respectively. By joining these points are obtain the line $x+y=8$ . So, the region containing the origin represents the solution set of the equation $x+y\leq 8.$ Clearly, $(0,0)$ satisfies the equation $x+y\leq 8$ . So, the region in xy-plan which does not contain the origin represents the solution set of the equation $x+y\leq 8.$

Region presented by $x+4y=12$ . The line $x+4y=12$ meets the coordinate axes at $C(12,0)$ and $D(0,3)$ respectively. By joining these points are obtain the line $x+4y=12$ . So, the region containing the origin represents the solution set of the equation $x+4y=12$ Clearly, $(0,0)$ satisfies the equation $x+4y=12$ . So, the region in xy-plan which does not contain the origin represents the solution set of the equation $x+4y=12$ .

The line $5x+4y=20$ is the line that passes through $E(0,4)$ and $F(0,\frac{5}{2})$ . Region presented by $x\geq 0$ and $y\geq 0$ . Since the every point in the first quadrant satisfies these equations. So, the first quadrant is the region represented by the equation $x\geq 0$ and $y\geq 0$