Different Types of Linear Programming Problems
Linear Inequalities and Linear Programming

88581 If \(4 x+5 y \geq 20, x \leq 6, y \leq 4, x \geq 0, y \geq 0\) forms

1 Triangle
2 Square
3 Pentagon
4 Quadrilateral
Linear Inequalities and Linear Programming

88582 Which of the following points is the point in the solution set of constraints
\(x+2 y \geq 11,3 x+4 y \leq 30,2 x+5 y \leq 30, x \geq 0\)
y of an LPP ?

1 \((3,4)\)
2 \((4,3)\)
3 \((2,3)\)
4 \((3,2)\)
Linear Inequalities and Linear Programming

88583 The minimum value of \(Z=2 x_{1}+3 x_{2}\) subject to the constraints \(2 x_{1}+7 x_{2} \geq 22, x_{1}+x_{2} \geq 6,5 x_{1}+x_{2}\) \(\geq 10\) and \(x_{1}, x_{2} \geq 0\) is

1 14
2 20
3 10
4 16
Linear Inequalities and Linear Programming

88584 Given the LPP Minimize \(f=2 x_{1}-x_{2}\)
\(\mathbf{x}_{1} \geq \mathbf{0}, \mathbf{x}_{2} \geq \mathbf{0}\)
\(\mathbf{x}_{1}+\mathbf{x}_{2} \geq \mathbf{5}\)
\(-\mathbf{x}_{1}+\mathbf{x}_{2} \leq \mathbf{1}\)
\(\mathbf{5} x_{1}+\mathbf{4} x_{2} \leq \mathbf{4 0}\)
The solution is

1 1
2 -1
3 2
4 -2
Linear Inequalities and Linear Programming

88581 If \(4 x+5 y \geq 20, x \leq 6, y \leq 4, x \geq 0, y \geq 0\) forms

1 Triangle
2 Square
3 Pentagon
4 Quadrilateral
Linear Inequalities and Linear Programming

88582 Which of the following points is the point in the solution set of constraints
\(x+2 y \geq 11,3 x+4 y \leq 30,2 x+5 y \leq 30, x \geq 0\)
y of an LPP ?

1 \((3,4)\)
2 \((4,3)\)
3 \((2,3)\)
4 \((3,2)\)
Linear Inequalities and Linear Programming

88583 The minimum value of \(Z=2 x_{1}+3 x_{2}\) subject to the constraints \(2 x_{1}+7 x_{2} \geq 22, x_{1}+x_{2} \geq 6,5 x_{1}+x_{2}\) \(\geq 10\) and \(x_{1}, x_{2} \geq 0\) is

1 14
2 20
3 10
4 16
Linear Inequalities and Linear Programming

88584 Given the LPP Minimize \(f=2 x_{1}-x_{2}\)
\(\mathbf{x}_{1} \geq \mathbf{0}, \mathbf{x}_{2} \geq \mathbf{0}\)
\(\mathbf{x}_{1}+\mathbf{x}_{2} \geq \mathbf{5}\)
\(-\mathbf{x}_{1}+\mathbf{x}_{2} \leq \mathbf{1}\)
\(\mathbf{5} x_{1}+\mathbf{4} x_{2} \leq \mathbf{4 0}\)
The solution is

1 1
2 -1
3 2
4 -2
Linear Inequalities and Linear Programming

88581 If \(4 x+5 y \geq 20, x \leq 6, y \leq 4, x \geq 0, y \geq 0\) forms

1 Triangle
2 Square
3 Pentagon
4 Quadrilateral
Linear Inequalities and Linear Programming

88582 Which of the following points is the point in the solution set of constraints
\(x+2 y \geq 11,3 x+4 y \leq 30,2 x+5 y \leq 30, x \geq 0\)
y of an LPP ?

1 \((3,4)\)
2 \((4,3)\)
3 \((2,3)\)
4 \((3,2)\)
Linear Inequalities and Linear Programming

88583 The minimum value of \(Z=2 x_{1}+3 x_{2}\) subject to the constraints \(2 x_{1}+7 x_{2} \geq 22, x_{1}+x_{2} \geq 6,5 x_{1}+x_{2}\) \(\geq 10\) and \(x_{1}, x_{2} \geq 0\) is

1 14
2 20
3 10
4 16
Linear Inequalities and Linear Programming

88584 Given the LPP Minimize \(f=2 x_{1}-x_{2}\)
\(\mathbf{x}_{1} \geq \mathbf{0}, \mathbf{x}_{2} \geq \mathbf{0}\)
\(\mathbf{x}_{1}+\mathbf{x}_{2} \geq \mathbf{5}\)
\(-\mathbf{x}_{1}+\mathbf{x}_{2} \leq \mathbf{1}\)
\(\mathbf{5} x_{1}+\mathbf{4} x_{2} \leq \mathbf{4 0}\)
The solution is

1 1
2 -1
3 2
4 -2
Linear Inequalities and Linear Programming

88581 If \(4 x+5 y \geq 20, x \leq 6, y \leq 4, x \geq 0, y \geq 0\) forms

1 Triangle
2 Square
3 Pentagon
4 Quadrilateral
Linear Inequalities and Linear Programming

88582 Which of the following points is the point in the solution set of constraints
\(x+2 y \geq 11,3 x+4 y \leq 30,2 x+5 y \leq 30, x \geq 0\)
y of an LPP ?

1 \((3,4)\)
2 \((4,3)\)
3 \((2,3)\)
4 \((3,2)\)
Linear Inequalities and Linear Programming

88583 The minimum value of \(Z=2 x_{1}+3 x_{2}\) subject to the constraints \(2 x_{1}+7 x_{2} \geq 22, x_{1}+x_{2} \geq 6,5 x_{1}+x_{2}\) \(\geq 10\) and \(x_{1}, x_{2} \geq 0\) is

1 14
2 20
3 10
4 16
Linear Inequalities and Linear Programming

88584 Given the LPP Minimize \(f=2 x_{1}-x_{2}\)
\(\mathbf{x}_{1} \geq \mathbf{0}, \mathbf{x}_{2} \geq \mathbf{0}\)
\(\mathbf{x}_{1}+\mathbf{x}_{2} \geq \mathbf{5}\)
\(-\mathbf{x}_{1}+\mathbf{x}_{2} \leq \mathbf{1}\)
\(\mathbf{5} x_{1}+\mathbf{4} x_{2} \leq \mathbf{4 0}\)
The solution is

1 1
2 -1
3 2
4 -2