Different Types of Linear Programming Problems
Linear Inequalities and Linear Programming

88586 Let \(z=x+y\), then the maximum of \(z\) subject to constraints \(y \geq|x|-1\)
\(\mathbf{y} \leq \mathbf{1}-|\mathbf{x}|\), is :
\(\mathbf{x} \geq \mathbf{0}, \mathbf{y} \geq \mathbf{0}\)

1 0
2 1
3 2
4 -1
Linear Inequalities and Linear Programming

88587 The minimum value of the function \(Z=2 x-y\) subjected to be constraints \(x+y \leq 5, x+2 y \geq 8, x \geq 0, y \geq 0\) is

1 \(Z=5\)
2 \(Z=1\)
3 \(Z=-4\)
4 \(Z=-5\)
Linear Inequalities and Linear Programming

88588 Minimize \(z=x+3 y\) subject to the constraints \(\mathbf{x}+\mathbf{y} \geq \mathbf{1 0}\)
\(2 \mathbf{x}-\mathbf{y} \geq \mathbf{0}\)
\(\mathbf{x}, \mathbf{y} \geq \mathbf{0}\)
In the above Linear Programming Problem, the objective function is

1 \(z=x+2 y\)
2 \(z=2 x-y\)
3 \(z=x+y\)
4 \(z=x+3 y\)
Linear Inequalities and Linear Programming

88589 Zahida has 31 days to stitch clothes for a showroom. The blue designs can be sewn at a rate of 4 units per day while the white ones at a rate of 7 units per day. The clothes can be up to 96 units total. The cost for her to do the blue design is Rs. 80 per unit and that of the white one is Rs. 120 per unit. Which one of the following can be the linear programming problem to minimize the cost \((Z)\) for the blue and white design clothes sewn by her for the showroom? [b = number of units of blue designs, \(w=\) Number of units of white designs]

1 Minimize, \(\mathrm{Z}=4 \mathrm{~b}+72\), \(\mathrm{w}\) Subject to \(\mathrm{b}+\mathrm{w} \leq\) \(96, \mathrm{~b} / 80+\mathrm{w} / 120 \leq 31, \mathrm{~b}, \mathrm{w} \geq 0\)
2 Minimize, \(Z=80 b+120 w\) Subject to \(b+w \leq\) \(96, \mathrm{~b} / 4+\mathrm{w} / 7 \leq 31, \mathrm{~b}, \mathrm{w} \geq 0\)
3 Minimize, \(\mathrm{Z}=80 \mathrm{~b}+120 \mathrm{w}\) Subject to \(\mathrm{b}+\mathrm{w} \leq\) \(96,4 b+7 w \leq 31, b, w \geq 0\)
4 Minimize, \(\mathrm{Z}=\mathrm{b}+\mathrm{w}\) Subject to \(4 \mathrm{~b}+7 \mathrm{w} \leq 96\), \(80 b+120 w \leq 31, b, w \geq 0\)
Linear Inequalities and Linear Programming

88591 Minimize objective function \(z=3 x+2 y\) subject to the constraints :
\(x+y \geq 8, x+5 y \leq 15, x \geq 0, y \geq 0\) is :

1 15
2 6
3 24
4 No feasible region and hence no feasible solution
Linear Inequalities and Linear Programming

88586 Let \(z=x+y\), then the maximum of \(z\) subject to constraints \(y \geq|x|-1\)
\(\mathbf{y} \leq \mathbf{1}-|\mathbf{x}|\), is :
\(\mathbf{x} \geq \mathbf{0}, \mathbf{y} \geq \mathbf{0}\)

1 0
2 1
3 2
4 -1
Linear Inequalities and Linear Programming

88587 The minimum value of the function \(Z=2 x-y\) subjected to be constraints \(x+y \leq 5, x+2 y \geq 8, x \geq 0, y \geq 0\) is

1 \(Z=5\)
2 \(Z=1\)
3 \(Z=-4\)
4 \(Z=-5\)
Linear Inequalities and Linear Programming

88588 Minimize \(z=x+3 y\) subject to the constraints \(\mathbf{x}+\mathbf{y} \geq \mathbf{1 0}\)
\(2 \mathbf{x}-\mathbf{y} \geq \mathbf{0}\)
\(\mathbf{x}, \mathbf{y} \geq \mathbf{0}\)
In the above Linear Programming Problem, the objective function is

1 \(z=x+2 y\)
2 \(z=2 x-y\)
3 \(z=x+y\)
4 \(z=x+3 y\)
Linear Inequalities and Linear Programming

88589 Zahida has 31 days to stitch clothes for a showroom. The blue designs can be sewn at a rate of 4 units per day while the white ones at a rate of 7 units per day. The clothes can be up to 96 units total. The cost for her to do the blue design is Rs. 80 per unit and that of the white one is Rs. 120 per unit. Which one of the following can be the linear programming problem to minimize the cost \((Z)\) for the blue and white design clothes sewn by her for the showroom? [b = number of units of blue designs, \(w=\) Number of units of white designs]

1 Minimize, \(\mathrm{Z}=4 \mathrm{~b}+72\), \(\mathrm{w}\) Subject to \(\mathrm{b}+\mathrm{w} \leq\) \(96, \mathrm{~b} / 80+\mathrm{w} / 120 \leq 31, \mathrm{~b}, \mathrm{w} \geq 0\)
2 Minimize, \(Z=80 b+120 w\) Subject to \(b+w \leq\) \(96, \mathrm{~b} / 4+\mathrm{w} / 7 \leq 31, \mathrm{~b}, \mathrm{w} \geq 0\)
3 Minimize, \(\mathrm{Z}=80 \mathrm{~b}+120 \mathrm{w}\) Subject to \(\mathrm{b}+\mathrm{w} \leq\) \(96,4 b+7 w \leq 31, b, w \geq 0\)
4 Minimize, \(\mathrm{Z}=\mathrm{b}+\mathrm{w}\) Subject to \(4 \mathrm{~b}+7 \mathrm{w} \leq 96\), \(80 b+120 w \leq 31, b, w \geq 0\)
Linear Inequalities and Linear Programming

88591 Minimize objective function \(z=3 x+2 y\) subject to the constraints :
\(x+y \geq 8, x+5 y \leq 15, x \geq 0, y \geq 0\) is :

1 15
2 6
3 24
4 No feasible region and hence no feasible solution
Linear Inequalities and Linear Programming

88586 Let \(z=x+y\), then the maximum of \(z\) subject to constraints \(y \geq|x|-1\)
\(\mathbf{y} \leq \mathbf{1}-|\mathbf{x}|\), is :
\(\mathbf{x} \geq \mathbf{0}, \mathbf{y} \geq \mathbf{0}\)

1 0
2 1
3 2
4 -1
Linear Inequalities and Linear Programming

88587 The minimum value of the function \(Z=2 x-y\) subjected to be constraints \(x+y \leq 5, x+2 y \geq 8, x \geq 0, y \geq 0\) is

1 \(Z=5\)
2 \(Z=1\)
3 \(Z=-4\)
4 \(Z=-5\)
Linear Inequalities and Linear Programming

88588 Minimize \(z=x+3 y\) subject to the constraints \(\mathbf{x}+\mathbf{y} \geq \mathbf{1 0}\)
\(2 \mathbf{x}-\mathbf{y} \geq \mathbf{0}\)
\(\mathbf{x}, \mathbf{y} \geq \mathbf{0}\)
In the above Linear Programming Problem, the objective function is

1 \(z=x+2 y\)
2 \(z=2 x-y\)
3 \(z=x+y\)
4 \(z=x+3 y\)
Linear Inequalities and Linear Programming

88589 Zahida has 31 days to stitch clothes for a showroom. The blue designs can be sewn at a rate of 4 units per day while the white ones at a rate of 7 units per day. The clothes can be up to 96 units total. The cost for her to do the blue design is Rs. 80 per unit and that of the white one is Rs. 120 per unit. Which one of the following can be the linear programming problem to minimize the cost \((Z)\) for the blue and white design clothes sewn by her for the showroom? [b = number of units of blue designs, \(w=\) Number of units of white designs]

1 Minimize, \(\mathrm{Z}=4 \mathrm{~b}+72\), \(\mathrm{w}\) Subject to \(\mathrm{b}+\mathrm{w} \leq\) \(96, \mathrm{~b} / 80+\mathrm{w} / 120 \leq 31, \mathrm{~b}, \mathrm{w} \geq 0\)
2 Minimize, \(Z=80 b+120 w\) Subject to \(b+w \leq\) \(96, \mathrm{~b} / 4+\mathrm{w} / 7 \leq 31, \mathrm{~b}, \mathrm{w} \geq 0\)
3 Minimize, \(\mathrm{Z}=80 \mathrm{~b}+120 \mathrm{w}\) Subject to \(\mathrm{b}+\mathrm{w} \leq\) \(96,4 b+7 w \leq 31, b, w \geq 0\)
4 Minimize, \(\mathrm{Z}=\mathrm{b}+\mathrm{w}\) Subject to \(4 \mathrm{~b}+7 \mathrm{w} \leq 96\), \(80 b+120 w \leq 31, b, w \geq 0\)
Linear Inequalities and Linear Programming

88591 Minimize objective function \(z=3 x+2 y\) subject to the constraints :
\(x+y \geq 8, x+5 y \leq 15, x \geq 0, y \geq 0\) is :

1 15
2 6
3 24
4 No feasible region and hence no feasible solution
Linear Inequalities and Linear Programming

88586 Let \(z=x+y\), then the maximum of \(z\) subject to constraints \(y \geq|x|-1\)
\(\mathbf{y} \leq \mathbf{1}-|\mathbf{x}|\), is :
\(\mathbf{x} \geq \mathbf{0}, \mathbf{y} \geq \mathbf{0}\)

1 0
2 1
3 2
4 -1
Linear Inequalities and Linear Programming

88587 The minimum value of the function \(Z=2 x-y\) subjected to be constraints \(x+y \leq 5, x+2 y \geq 8, x \geq 0, y \geq 0\) is

1 \(Z=5\)
2 \(Z=1\)
3 \(Z=-4\)
4 \(Z=-5\)
Linear Inequalities and Linear Programming

88588 Minimize \(z=x+3 y\) subject to the constraints \(\mathbf{x}+\mathbf{y} \geq \mathbf{1 0}\)
\(2 \mathbf{x}-\mathbf{y} \geq \mathbf{0}\)
\(\mathbf{x}, \mathbf{y} \geq \mathbf{0}\)
In the above Linear Programming Problem, the objective function is

1 \(z=x+2 y\)
2 \(z=2 x-y\)
3 \(z=x+y\)
4 \(z=x+3 y\)
Linear Inequalities and Linear Programming

88589 Zahida has 31 days to stitch clothes for a showroom. The blue designs can be sewn at a rate of 4 units per day while the white ones at a rate of 7 units per day. The clothes can be up to 96 units total. The cost for her to do the blue design is Rs. 80 per unit and that of the white one is Rs. 120 per unit. Which one of the following can be the linear programming problem to minimize the cost \((Z)\) for the blue and white design clothes sewn by her for the showroom? [b = number of units of blue designs, \(w=\) Number of units of white designs]

1 Minimize, \(\mathrm{Z}=4 \mathrm{~b}+72\), \(\mathrm{w}\) Subject to \(\mathrm{b}+\mathrm{w} \leq\) \(96, \mathrm{~b} / 80+\mathrm{w} / 120 \leq 31, \mathrm{~b}, \mathrm{w} \geq 0\)
2 Minimize, \(Z=80 b+120 w\) Subject to \(b+w \leq\) \(96, \mathrm{~b} / 4+\mathrm{w} / 7 \leq 31, \mathrm{~b}, \mathrm{w} \geq 0\)
3 Minimize, \(\mathrm{Z}=80 \mathrm{~b}+120 \mathrm{w}\) Subject to \(\mathrm{b}+\mathrm{w} \leq\) \(96,4 b+7 w \leq 31, b, w \geq 0\)
4 Minimize, \(\mathrm{Z}=\mathrm{b}+\mathrm{w}\) Subject to \(4 \mathrm{~b}+7 \mathrm{w} \leq 96\), \(80 b+120 w \leq 31, b, w \geq 0\)
Linear Inequalities and Linear Programming

88591 Minimize objective function \(z=3 x+2 y\) subject to the constraints :
\(x+y \geq 8, x+5 y \leq 15, x \geq 0, y \geq 0\) is :

1 15
2 6
3 24
4 No feasible region and hence no feasible solution
Linear Inequalities and Linear Programming

88586 Let \(z=x+y\), then the maximum of \(z\) subject to constraints \(y \geq|x|-1\)
\(\mathbf{y} \leq \mathbf{1}-|\mathbf{x}|\), is :
\(\mathbf{x} \geq \mathbf{0}, \mathbf{y} \geq \mathbf{0}\)

1 0
2 1
3 2
4 -1
Linear Inequalities and Linear Programming

88587 The minimum value of the function \(Z=2 x-y\) subjected to be constraints \(x+y \leq 5, x+2 y \geq 8, x \geq 0, y \geq 0\) is

1 \(Z=5\)
2 \(Z=1\)
3 \(Z=-4\)
4 \(Z=-5\)
Linear Inequalities and Linear Programming

88588 Minimize \(z=x+3 y\) subject to the constraints \(\mathbf{x}+\mathbf{y} \geq \mathbf{1 0}\)
\(2 \mathbf{x}-\mathbf{y} \geq \mathbf{0}\)
\(\mathbf{x}, \mathbf{y} \geq \mathbf{0}\)
In the above Linear Programming Problem, the objective function is

1 \(z=x+2 y\)
2 \(z=2 x-y\)
3 \(z=x+y\)
4 \(z=x+3 y\)
Linear Inequalities and Linear Programming

88589 Zahida has 31 days to stitch clothes for a showroom. The blue designs can be sewn at a rate of 4 units per day while the white ones at a rate of 7 units per day. The clothes can be up to 96 units total. The cost for her to do the blue design is Rs. 80 per unit and that of the white one is Rs. 120 per unit. Which one of the following can be the linear programming problem to minimize the cost \((Z)\) for the blue and white design clothes sewn by her for the showroom? [b = number of units of blue designs, \(w=\) Number of units of white designs]

1 Minimize, \(\mathrm{Z}=4 \mathrm{~b}+72\), \(\mathrm{w}\) Subject to \(\mathrm{b}+\mathrm{w} \leq\) \(96, \mathrm{~b} / 80+\mathrm{w} / 120 \leq 31, \mathrm{~b}, \mathrm{w} \geq 0\)
2 Minimize, \(Z=80 b+120 w\) Subject to \(b+w \leq\) \(96, \mathrm{~b} / 4+\mathrm{w} / 7 \leq 31, \mathrm{~b}, \mathrm{w} \geq 0\)
3 Minimize, \(\mathrm{Z}=80 \mathrm{~b}+120 \mathrm{w}\) Subject to \(\mathrm{b}+\mathrm{w} \leq\) \(96,4 b+7 w \leq 31, b, w \geq 0\)
4 Minimize, \(\mathrm{Z}=\mathrm{b}+\mathrm{w}\) Subject to \(4 \mathrm{~b}+7 \mathrm{w} \leq 96\), \(80 b+120 w \leq 31, b, w \geq 0\)
Linear Inequalities and Linear Programming

88591 Minimize objective function \(z=3 x+2 y\) subject to the constraints :
\(x+y \geq 8, x+5 y \leq 15, x \geq 0, y \geq 0\) is :

1 15
2 6
3 24
4 No feasible region and hence no feasible solution