Need solution for RD Sharma maths class 12 chapter Linear Programming exercise 29.2 question 7
Answer:
The optimal value of z is 56.
Hint:
Plot the points on the graph.
Given:
Solution:
First, we will convert the given in equations into equations, we obtain the following equations
and
Region presented by . The line meets the coordinate axes at and respectively. By joining these points are obtain the line . So, the region containing the
origin represents the solution set of the equation Clearly, 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 and respectively. By joining these points are obtain the line . So, the region containing
the origin represents the solution set of the equation Clearly, satisfies the equation . So, the region contain the origin represents the solution set of the equation
Region presented by and . Since the every point in the first quadrant satisfies these equations. So, the first quadrant is the region represented by the equation and .
The feasible region determined by the system of constraints,
and are as follows
The corner points of the feasible region are
The value of z at these corner points are as follows
Corner Points | |
Therefore, the maximum value of objective function z is 56 at the point The means at and Thus, the optimal of z is 56.