Different Types of Linear Programming Problems
Linear Inequalities and Linear Programming

88569 For the LPP, maximise \(z=x+4 y\) subject to the constraints \(x+2 y \leq 2, x+2 y \geq 8, x, y \geq 0\).

1 \(Z_{\max }=4\)
2 \(\mathrm{Z}_{\max }=8\)
3 \(Z_{\max }=16\)
4 has no feasible solution
Linear Inequalities and Linear Programming

88570 If \(x+y \leq 2, x \geq 0, y \geq 0\), the point at which maximum value of \(3 x+2 y\) attained will be

1 \((0,2)\)
2 \((0,0)\)
3 \((2,0)\)
4 \(\left(\frac{1}{2}, \frac{1}{2}\right)\)
Linear Inequalities and Linear Programming

88572 The maximum value of \(z=3 x+4 y\) subject to the constraints \(x+y \leq 40, \quad x+2 y \leq 60, \quad x \geq 0\), \(\mathbf{y} \geq \mathbf{0}\) is

1 120
2 140
3 100
4 160
Linear Inequalities and Linear Programming

88573 Minimize \(\mathbf{Z}=\sum_{\mathrm{j}=1}^{\mathrm{n}} \sum_{\mathrm{i}=1}^{\mathrm{m}} \mathbf{c}_{\mathrm{ij}} \mathbf{x}_{\mathrm{ij}}\)
Subject to \(\sum_{i=1}^{m} x_{i j}=b_{j}, j=1,2, \ldots ., n\)
\(\sum_{j=1}^{n} x_{i j}=b_{j}, i=1,2, \ldots ., m\) is a LPP with number of constraints

1 \(m-n\)
2 \(\mathrm{mn}\)
3 \(\mathrm{m}+\mathrm{n}\)
4 \(\frac{m}{n}\)
Linear Inequalities and Linear Programming

88574 Which of the following statements is correct?

1 Every L.P.P. admits an optimal solution.
2 A L.P.P. admits a unique optimal solution.
3 If a L.P.P. admits two optimal solutions, it has an infinite number of optimal solutions.
4 The set of all feasible solutions of a L.P.P. is not a convex set.
Linear Inequalities and Linear Programming

88569 For the LPP, maximise \(z=x+4 y\) subject to the constraints \(x+2 y \leq 2, x+2 y \geq 8, x, y \geq 0\).

1 \(Z_{\max }=4\)
2 \(\mathrm{Z}_{\max }=8\)
3 \(Z_{\max }=16\)
4 has no feasible solution
Linear Inequalities and Linear Programming

88570 If \(x+y \leq 2, x \geq 0, y \geq 0\), the point at which maximum value of \(3 x+2 y\) attained will be

1 \((0,2)\)
2 \((0,0)\)
3 \((2,0)\)
4 \(\left(\frac{1}{2}, \frac{1}{2}\right)\)
Linear Inequalities and Linear Programming

88572 The maximum value of \(z=3 x+4 y\) subject to the constraints \(x+y \leq 40, \quad x+2 y \leq 60, \quad x \geq 0\), \(\mathbf{y} \geq \mathbf{0}\) is

1 120
2 140
3 100
4 160
Linear Inequalities and Linear Programming

88573 Minimize \(\mathbf{Z}=\sum_{\mathrm{j}=1}^{\mathrm{n}} \sum_{\mathrm{i}=1}^{\mathrm{m}} \mathbf{c}_{\mathrm{ij}} \mathbf{x}_{\mathrm{ij}}\)
Subject to \(\sum_{i=1}^{m} x_{i j}=b_{j}, j=1,2, \ldots ., n\)
\(\sum_{j=1}^{n} x_{i j}=b_{j}, i=1,2, \ldots ., m\) is a LPP with number of constraints

1 \(m-n\)
2 \(\mathrm{mn}\)
3 \(\mathrm{m}+\mathrm{n}\)
4 \(\frac{m}{n}\)
Linear Inequalities and Linear Programming

88574 Which of the following statements is correct?

1 Every L.P.P. admits an optimal solution.
2 A L.P.P. admits a unique optimal solution.
3 If a L.P.P. admits two optimal solutions, it has an infinite number of optimal solutions.
4 The set of all feasible solutions of a L.P.P. is not a convex set.
Linear Inequalities and Linear Programming

88569 For the LPP, maximise \(z=x+4 y\) subject to the constraints \(x+2 y \leq 2, x+2 y \geq 8, x, y \geq 0\).

1 \(Z_{\max }=4\)
2 \(\mathrm{Z}_{\max }=8\)
3 \(Z_{\max }=16\)
4 has no feasible solution
Linear Inequalities and Linear Programming

88570 If \(x+y \leq 2, x \geq 0, y \geq 0\), the point at which maximum value of \(3 x+2 y\) attained will be

1 \((0,2)\)
2 \((0,0)\)
3 \((2,0)\)
4 \(\left(\frac{1}{2}, \frac{1}{2}\right)\)
Linear Inequalities and Linear Programming

88572 The maximum value of \(z=3 x+4 y\) subject to the constraints \(x+y \leq 40, \quad x+2 y \leq 60, \quad x \geq 0\), \(\mathbf{y} \geq \mathbf{0}\) is

1 120
2 140
3 100
4 160
Linear Inequalities and Linear Programming

88573 Minimize \(\mathbf{Z}=\sum_{\mathrm{j}=1}^{\mathrm{n}} \sum_{\mathrm{i}=1}^{\mathrm{m}} \mathbf{c}_{\mathrm{ij}} \mathbf{x}_{\mathrm{ij}}\)
Subject to \(\sum_{i=1}^{m} x_{i j}=b_{j}, j=1,2, \ldots ., n\)
\(\sum_{j=1}^{n} x_{i j}=b_{j}, i=1,2, \ldots ., m\) is a LPP with number of constraints

1 \(m-n\)
2 \(\mathrm{mn}\)
3 \(\mathrm{m}+\mathrm{n}\)
4 \(\frac{m}{n}\)
Linear Inequalities and Linear Programming

88574 Which of the following statements is correct?

1 Every L.P.P. admits an optimal solution.
2 A L.P.P. admits a unique optimal solution.
3 If a L.P.P. admits two optimal solutions, it has an infinite number of optimal solutions.
4 The set of all feasible solutions of a L.P.P. is not a convex set.
Linear Inequalities and Linear Programming

88569 For the LPP, maximise \(z=x+4 y\) subject to the constraints \(x+2 y \leq 2, x+2 y \geq 8, x, y \geq 0\).

1 \(Z_{\max }=4\)
2 \(\mathrm{Z}_{\max }=8\)
3 \(Z_{\max }=16\)
4 has no feasible solution
Linear Inequalities and Linear Programming

88570 If \(x+y \leq 2, x \geq 0, y \geq 0\), the point at which maximum value of \(3 x+2 y\) attained will be

1 \((0,2)\)
2 \((0,0)\)
3 \((2,0)\)
4 \(\left(\frac{1}{2}, \frac{1}{2}\right)\)
Linear Inequalities and Linear Programming

88572 The maximum value of \(z=3 x+4 y\) subject to the constraints \(x+y \leq 40, \quad x+2 y \leq 60, \quad x \geq 0\), \(\mathbf{y} \geq \mathbf{0}\) is

1 120
2 140
3 100
4 160
Linear Inequalities and Linear Programming

88573 Minimize \(\mathbf{Z}=\sum_{\mathrm{j}=1}^{\mathrm{n}} \sum_{\mathrm{i}=1}^{\mathrm{m}} \mathbf{c}_{\mathrm{ij}} \mathbf{x}_{\mathrm{ij}}\)
Subject to \(\sum_{i=1}^{m} x_{i j}=b_{j}, j=1,2, \ldots ., n\)
\(\sum_{j=1}^{n} x_{i j}=b_{j}, i=1,2, \ldots ., m\) is a LPP with number of constraints

1 \(m-n\)
2 \(\mathrm{mn}\)
3 \(\mathrm{m}+\mathrm{n}\)
4 \(\frac{m}{n}\)
Linear Inequalities and Linear Programming

88574 Which of the following statements is correct?

1 Every L.P.P. admits an optimal solution.
2 A L.P.P. admits a unique optimal solution.
3 If a L.P.P. admits two optimal solutions, it has an infinite number of optimal solutions.
4 The set of all feasible solutions of a L.P.P. is not a convex set.
Linear Inequalities and Linear Programming

88569 For the LPP, maximise \(z=x+4 y\) subject to the constraints \(x+2 y \leq 2, x+2 y \geq 8, x, y \geq 0\).

1 \(Z_{\max }=4\)
2 \(\mathrm{Z}_{\max }=8\)
3 \(Z_{\max }=16\)
4 has no feasible solution
Linear Inequalities and Linear Programming

88570 If \(x+y \leq 2, x \geq 0, y \geq 0\), the point at which maximum value of \(3 x+2 y\) attained will be

1 \((0,2)\)
2 \((0,0)\)
3 \((2,0)\)
4 \(\left(\frac{1}{2}, \frac{1}{2}\right)\)
Linear Inequalities and Linear Programming

88572 The maximum value of \(z=3 x+4 y\) subject to the constraints \(x+y \leq 40, \quad x+2 y \leq 60, \quad x \geq 0\), \(\mathbf{y} \geq \mathbf{0}\) is

1 120
2 140
3 100
4 160
Linear Inequalities and Linear Programming

88573 Minimize \(\mathbf{Z}=\sum_{\mathrm{j}=1}^{\mathrm{n}} \sum_{\mathrm{i}=1}^{\mathrm{m}} \mathbf{c}_{\mathrm{ij}} \mathbf{x}_{\mathrm{ij}}\)
Subject to \(\sum_{i=1}^{m} x_{i j}=b_{j}, j=1,2, \ldots ., n\)
\(\sum_{j=1}^{n} x_{i j}=b_{j}, i=1,2, \ldots ., m\) is a LPP with number of constraints

1 \(m-n\)
2 \(\mathrm{mn}\)
3 \(\mathrm{m}+\mathrm{n}\)
4 \(\frac{m}{n}\)
Linear Inequalities and Linear Programming

88574 Which of the following statements is correct?

1 Every L.P.P. admits an optimal solution.
2 A L.P.P. admits a unique optimal solution.
3 If a L.P.P. admits two optimal solutions, it has an infinite number of optimal solutions.
4 The set of all feasible solutions of a L.P.P. is not a convex set.