Okay so suppose only dotted lines(rather that solid lines) border a solution region.The given linear objective function is Q=x+y, which is based on contiuous variables. Can the obejective function have a maximum or a minimum value??
Q is a function of x and y. There is no limit to how high or how low Q can go. Therefore there is no maximum or minimum value
z=4x+3y
2x+3y<=6
3x-2y<=9
x+5y<=20
x>=0,y>=0
To determine whether the objective function Q = x + y has a maximum or minimum value, we need more information about the constraints and the feasible region.
1. Constraints: The constraints define the boundaries of the feasible region. They can be represented by linear inequalities such as Ax + By ≤ C. Please provide the specific constraints for your problem.
2. Feasible Region: The feasible region is the set of all points that satisfy the constraints. It can be determined by shading the region that satisfies the inequalities on a graph.
Once we have identified the feasible region, we can determine whether the objective function has a maximum or minimum value.
Generally, in linear programming problems, if the feasible region is bounded (i.e., it has a finite area), then the objective function will have both a maximum and minimum value. The maximum value occurs at one of the vertices of the feasible region, while the minimum value occurs at another vertex.
However, if the feasible region is unbounded (i.e., it extends infinitely in one or more directions), then the objective function may not have a maximum or minimum value. In this case, it would be said that the objective function is unbounded.
Therefore, it is important to determine the feasible region and its boundaries in order to determine whether the objective function has a maximum or minimum value.