Graphical Solution of Linear Inequalities of Two Variables
Linear Inequalities and Linear Programming

88565 Consider the linear programming problem
Max \(Z=4 x+y\)
Subject to \(\quad \mathbf{x}+\mathbf{y} \leq \mathbf{5 0}\)
\(\mathbf{x}+\mathbf{y} \geq \mathbf{1 0 0}\)
\(\mathbf{x}, \mathbf{y} \geq \mathbf{0}\)
The max value of \(Z\) is

1 0
2 50
3 100
4 does not exist
Linear Inequalities and Linear Programming

88566 Solve the system of linear equations \(x+y=1, x\) \(-2 \mathbf{y}=4\).

1 \(x=2, y=-5\)
2 \(x=1, y=2\)
3 \(x=2, y=-1\)
4 \(x=-1, y=2\)
Linear Inequalities and Linear Programming

88567 The solution set for the system of linear in equations
\(x+y \geq 1: 7 x+9 y \leq 63: x \leq 6, y \leq 5, x \geq 0\) and \(y \geq\)
0 is represented graphically by the figure (a)

1
2
3
4
Linear Inequalities and Linear Programming

88568 The feasible region for a L.P.P. is shown in the figure below. Let \(z=50 x+15 y\) be the objective function, then the maximum value of \(z\) is

1 900
2 1000
3 1250
4 1300
5 1520
Linear Inequalities and Linear Programming

88562 The region represented by the in equation system \(x, y \geq 0, y \leq 6, x+y \leq 3\) is

1 unbounded in first quadrant
2 unbounded in first and second quadrant
3 bounded in first quadrant
4 None of these
Linear Inequalities and Linear Programming

88565 Consider the linear programming problem
Max \(Z=4 x+y\)
Subject to \(\quad \mathbf{x}+\mathbf{y} \leq \mathbf{5 0}\)
\(\mathbf{x}+\mathbf{y} \geq \mathbf{1 0 0}\)
\(\mathbf{x}, \mathbf{y} \geq \mathbf{0}\)
The max value of \(Z\) is

1 0
2 50
3 100
4 does not exist
Linear Inequalities and Linear Programming

88566 Solve the system of linear equations \(x+y=1, x\) \(-2 \mathbf{y}=4\).

1 \(x=2, y=-5\)
2 \(x=1, y=2\)
3 \(x=2, y=-1\)
4 \(x=-1, y=2\)
Linear Inequalities and Linear Programming

88567 The solution set for the system of linear in equations
\(x+y \geq 1: 7 x+9 y \leq 63: x \leq 6, y \leq 5, x \geq 0\) and \(y \geq\)
0 is represented graphically by the figure (a)

1
2
3
4
Linear Inequalities and Linear Programming

88568 The feasible region for a L.P.P. is shown in the figure below. Let \(z=50 x+15 y\) be the objective function, then the maximum value of \(z\) is

1 900
2 1000
3 1250
4 1300
5 1520
Linear Inequalities and Linear Programming

88562 The region represented by the in equation system \(x, y \geq 0, y \leq 6, x+y \leq 3\) is

1 unbounded in first quadrant
2 unbounded in first and second quadrant
3 bounded in first quadrant
4 None of these
Linear Inequalities and Linear Programming

88565 Consider the linear programming problem
Max \(Z=4 x+y\)
Subject to \(\quad \mathbf{x}+\mathbf{y} \leq \mathbf{5 0}\)
\(\mathbf{x}+\mathbf{y} \geq \mathbf{1 0 0}\)
\(\mathbf{x}, \mathbf{y} \geq \mathbf{0}\)
The max value of \(Z\) is

1 0
2 50
3 100
4 does not exist
Linear Inequalities and Linear Programming

88566 Solve the system of linear equations \(x+y=1, x\) \(-2 \mathbf{y}=4\).

1 \(x=2, y=-5\)
2 \(x=1, y=2\)
3 \(x=2, y=-1\)
4 \(x=-1, y=2\)
Linear Inequalities and Linear Programming

88567 The solution set for the system of linear in equations
\(x+y \geq 1: 7 x+9 y \leq 63: x \leq 6, y \leq 5, x \geq 0\) and \(y \geq\)
0 is represented graphically by the figure (a)

1
2
3
4
Linear Inequalities and Linear Programming

88568 The feasible region for a L.P.P. is shown in the figure below. Let \(z=50 x+15 y\) be the objective function, then the maximum value of \(z\) is

1 900
2 1000
3 1250
4 1300
5 1520
Linear Inequalities and Linear Programming

88562 The region represented by the in equation system \(x, y \geq 0, y \leq 6, x+y \leq 3\) is

1 unbounded in first quadrant
2 unbounded in first and second quadrant
3 bounded in first quadrant
4 None of these
Linear Inequalities and Linear Programming

88565 Consider the linear programming problem
Max \(Z=4 x+y\)
Subject to \(\quad \mathbf{x}+\mathbf{y} \leq \mathbf{5 0}\)
\(\mathbf{x}+\mathbf{y} \geq \mathbf{1 0 0}\)
\(\mathbf{x}, \mathbf{y} \geq \mathbf{0}\)
The max value of \(Z\) is

1 0
2 50
3 100
4 does not exist
Linear Inequalities and Linear Programming

88566 Solve the system of linear equations \(x+y=1, x\) \(-2 \mathbf{y}=4\).

1 \(x=2, y=-5\)
2 \(x=1, y=2\)
3 \(x=2, y=-1\)
4 \(x=-1, y=2\)
Linear Inequalities and Linear Programming

88567 The solution set for the system of linear in equations
\(x+y \geq 1: 7 x+9 y \leq 63: x \leq 6, y \leq 5, x \geq 0\) and \(y \geq\)
0 is represented graphically by the figure (a)

1
2
3
4
Linear Inequalities and Linear Programming

88568 The feasible region for a L.P.P. is shown in the figure below. Let \(z=50 x+15 y\) be the objective function, then the maximum value of \(z\) is

1 900
2 1000
3 1250
4 1300
5 1520
Linear Inequalities and Linear Programming

88562 The region represented by the in equation system \(x, y \geq 0, y \leq 6, x+y \leq 3\) is

1 unbounded in first quadrant
2 unbounded in first and second quadrant
3 bounded in first quadrant
4 None of these
Linear Inequalities and Linear Programming

88565 Consider the linear programming problem
Max \(Z=4 x+y\)
Subject to \(\quad \mathbf{x}+\mathbf{y} \leq \mathbf{5 0}\)
\(\mathbf{x}+\mathbf{y} \geq \mathbf{1 0 0}\)
\(\mathbf{x}, \mathbf{y} \geq \mathbf{0}\)
The max value of \(Z\) is

1 0
2 50
3 100
4 does not exist
Linear Inequalities and Linear Programming

88566 Solve the system of linear equations \(x+y=1, x\) \(-2 \mathbf{y}=4\).

1 \(x=2, y=-5\)
2 \(x=1, y=2\)
3 \(x=2, y=-1\)
4 \(x=-1, y=2\)
Linear Inequalities and Linear Programming

88567 The solution set for the system of linear in equations
\(x+y \geq 1: 7 x+9 y \leq 63: x \leq 6, y \leq 5, x \geq 0\) and \(y \geq\)
0 is represented graphically by the figure (a)

1
2
3
4
Linear Inequalities and Linear Programming

88568 The feasible region for a L.P.P. is shown in the figure below. Let \(z=50 x+15 y\) be the objective function, then the maximum value of \(z\) is

1 900
2 1000
3 1250
4 1300
5 1520
Linear Inequalities and Linear Programming

88562 The region represented by the in equation system \(x, y \geq 0, y \leq 6, x+y \leq 3\) is

1 unbounded in first quadrant
2 unbounded in first and second quadrant
3 bounded in first quadrant
4 None of these