Explain solution RD Sharma class 12 chapter Linear Programming exercise 29.2 question 8 maths
Answer:
The optimal value of z is 140.
Hint:
Plot the points on the graph.
Given:
Solution:
We have to maximize
First, we will convert the given in equations into equations, we obtain the following equations
Region presented by The line meets the coordinate axes at A(40,0) and B(0,40 ) respectively. By joining these points are obtain the line . Clearly, (0,0) satisfies the equation . So, the region contain the origin represents the solution set of the equation
Region presented by . The line meets the coordinate axes at C(60,0) and D(0,30 ) respectively. By joining these points are obtain the line . Clearly, (0,0) does not satisfies the equation . So, the region in xy plane which does not contain the origin represents the solution set of the equation
The feasible region determined by the system of constraints,
are as follows
The corner points of the feasible region are
The value of z at these corner points are as follows
We see that the maximum value of objective function z is 140 at the point E(20,20). Which is at x=20 and y=20 is the optimal solution of the given LPP.
Thus, the optimal of z is 140.