1)Which term best describes the linear programming situation represented by x+y=2
why is the answer infeasible?
2)Describe the linear programming situation for this system of inequalities.
x < 1 y > 0 3x + y < 5 why is the answer unbounded?
1) The term that best describes the linear programming situation represented by the equation x + y = 2 is a constraint. The equation x + y = 2 is a mathematical representation of a constraint that limits the feasible region of a linear programming problem. In this case, it is a constraint that states that the sum of the variables x and y must be equal to 2.
The answer is infeasible because when we plot this equation on a graph, we see that it is a straight line. However, this line does not intersect with or touch the feasible region formed by the other constraints (if any) in the linear programming problem. Therefore, there exists no feasible solution that satisfies all the given constraints. Hence, the answer is infeasible.
2) The linear programming situation for the system of inequalities x < 1, y > 0, and 3x + y < 5 is characterized by multiple constraints. Each inequality represents a constraint that limits the feasible region of the linear programming problem.
For the first constraint, x < 1, it indicates that the variable x must have a value less than 1. This constraint restricts the feasible region to values of x that fall to the left of the vertical line x = 1 on the graph.
The second constraint, y > 0, states that the variable y must have a value greater than 0. This constraint limits the feasible region to values of y that lie above the horizontal line y = 0 on the graph.
Lastly, the third constraint, 3x + y < 5, represents a linear inequality that defines a boundary on the feasible region. When we plot this inequality on the graph, we find that it forms a line in the xy-plane. The feasible region is the area below this line.
The answer is unbounded because the feasible region extends infinitely in one or more directions. In this case, the feasible region extends infinitely towards the left and right on the x-axis, beyond the constraint x < 1. Therefore, there is no finite maximum or minimum value for the objective function, making the answer unbounded.