Different Types of Linear Programming Problems
Linear Inequalities and Linear Programming

88592 The maximum value of \(z=50 x+15 y\) subject to the constraints \(x+y \leq 60 ; 5 x+y \leq100 ; x \geq 0\); \(y \geq 0\) is at the point

1 \(125 \overline{0,(10,50)}\)
2 \(1000,(20,0)\)
3 \(900,(0,60)\)
4 \(2650,(50,10)\)
Linear Inequalities and Linear Programming

88594 The objective function \(z=4 x+5 y\) subject to \(2 x\) \(+\mathrm{y} \geq 7 ; 2 \mathrm{x}+3 \mathrm{y} \leq 15 ; \mathrm{y} \leq 3 ; \mathrm{x} \geq 0 ; \mathrm{y} \geq 0\) has minimum value at the point

1 on the parallel to \(\mathrm{X}\)-axis
2 on Y-axis
3 on X-axis
4 origin
Linear Inequalities and Linear Programming

88571 The constraints \(-x_{1}+x_{2} \leq 1, \quad-x_{1}+3 x_{2} \leq 9\), \(\mathbf{x}_{1}, \mathbf{x}_{2} \geq \mathbf{0}\) define on

1 Bounded feasible space.
2 Unbounded feasible space.
3 Both bounded and unbounded feasible space.
4 None of these
Linear Inequalities and Linear Programming

88585 An n-tuple \(\left(x_{1}, x_{2}, \ldots . . x_{n}\right)\) which satisfies all the constraints of a linear programming problem and for which the objective function is maximum (compared to all \(n\) - tuples which satisfy all the constraints) is called

1 a solution
2 a feasible solution
3 an optimal solution
4 an actual solution
Linear Inequalities and Linear Programming

88592 The maximum value of \(z=50 x+15 y\) subject to the constraints \(x+y \leq 60 ; 5 x+y \leq100 ; x \geq 0\); \(y \geq 0\) is at the point

1 \(125 \overline{0,(10,50)}\)
2 \(1000,(20,0)\)
3 \(900,(0,60)\)
4 \(2650,(50,10)\)
Linear Inequalities and Linear Programming

88594 The objective function \(z=4 x+5 y\) subject to \(2 x\) \(+\mathrm{y} \geq 7 ; 2 \mathrm{x}+3 \mathrm{y} \leq 15 ; \mathrm{y} \leq 3 ; \mathrm{x} \geq 0 ; \mathrm{y} \geq 0\) has minimum value at the point

1 on the parallel to \(\mathrm{X}\)-axis
2 on Y-axis
3 on X-axis
4 origin
Linear Inequalities and Linear Programming

88571 The constraints \(-x_{1}+x_{2} \leq 1, \quad-x_{1}+3 x_{2} \leq 9\), \(\mathbf{x}_{1}, \mathbf{x}_{2} \geq \mathbf{0}\) define on

1 Bounded feasible space.
2 Unbounded feasible space.
3 Both bounded and unbounded feasible space.
4 None of these
Linear Inequalities and Linear Programming

88585 An n-tuple \(\left(x_{1}, x_{2}, \ldots . . x_{n}\right)\) which satisfies all the constraints of a linear programming problem and for which the objective function is maximum (compared to all \(n\) - tuples which satisfy all the constraints) is called

1 a solution
2 a feasible solution
3 an optimal solution
4 an actual solution
Linear Inequalities and Linear Programming

88592 The maximum value of \(z=50 x+15 y\) subject to the constraints \(x+y \leq 60 ; 5 x+y \leq100 ; x \geq 0\); \(y \geq 0\) is at the point

1 \(125 \overline{0,(10,50)}\)
2 \(1000,(20,0)\)
3 \(900,(0,60)\)
4 \(2650,(50,10)\)
Linear Inequalities and Linear Programming

88594 The objective function \(z=4 x+5 y\) subject to \(2 x\) \(+\mathrm{y} \geq 7 ; 2 \mathrm{x}+3 \mathrm{y} \leq 15 ; \mathrm{y} \leq 3 ; \mathrm{x} \geq 0 ; \mathrm{y} \geq 0\) has minimum value at the point

1 on the parallel to \(\mathrm{X}\)-axis
2 on Y-axis
3 on X-axis
4 origin
Linear Inequalities and Linear Programming

88571 The constraints \(-x_{1}+x_{2} \leq 1, \quad-x_{1}+3 x_{2} \leq 9\), \(\mathbf{x}_{1}, \mathbf{x}_{2} \geq \mathbf{0}\) define on

1 Bounded feasible space.
2 Unbounded feasible space.
3 Both bounded and unbounded feasible space.
4 None of these
Linear Inequalities and Linear Programming

88585 An n-tuple \(\left(x_{1}, x_{2}, \ldots . . x_{n}\right)\) which satisfies all the constraints of a linear programming problem and for which the objective function is maximum (compared to all \(n\) - tuples which satisfy all the constraints) is called

1 a solution
2 a feasible solution
3 an optimal solution
4 an actual solution
Linear Inequalities and Linear Programming

88592 The maximum value of \(z=50 x+15 y\) subject to the constraints \(x+y \leq 60 ; 5 x+y \leq100 ; x \geq 0\); \(y \geq 0\) is at the point

1 \(125 \overline{0,(10,50)}\)
2 \(1000,(20,0)\)
3 \(900,(0,60)\)
4 \(2650,(50,10)\)
Linear Inequalities and Linear Programming

88594 The objective function \(z=4 x+5 y\) subject to \(2 x\) \(+\mathrm{y} \geq 7 ; 2 \mathrm{x}+3 \mathrm{y} \leq 15 ; \mathrm{y} \leq 3 ; \mathrm{x} \geq 0 ; \mathrm{y} \geq 0\) has minimum value at the point

1 on the parallel to \(\mathrm{X}\)-axis
2 on Y-axis
3 on X-axis
4 origin
Linear Inequalities and Linear Programming

88571 The constraints \(-x_{1}+x_{2} \leq 1, \quad-x_{1}+3 x_{2} \leq 9\), \(\mathbf{x}_{1}, \mathbf{x}_{2} \geq \mathbf{0}\) define on

1 Bounded feasible space.
2 Unbounded feasible space.
3 Both bounded and unbounded feasible space.
4 None of these
Linear Inequalities and Linear Programming

88585 An n-tuple \(\left(x_{1}, x_{2}, \ldots . . x_{n}\right)\) which satisfies all the constraints of a linear programming problem and for which the objective function is maximum (compared to all \(n\) - tuples which satisfy all the constraints) is called

1 a solution
2 a feasible solution
3 an optimal solution
4 an actual solution