1 \(2 x+5 y \geq 80, x+y \leq 20, x \geq 0, y \leq 0\)
2 \(2 x+5 y \geq 80, x+y \geq 20, x \geq 0, y \geq 0\)
3 \(2 x+5 y \leq 80, x+y \leq 20, x \geq 0, y \geq 0\)
4 \(2 x+5 y \leq 80, x+y \leq 20, x \leq 0, y \leq 0\)
Explanation:
(C) : Given, From above figure it is clear that- \(x, y \geq 0\) \(x+y=20\) \(x+y \leq 20\) \((0,0)\) \(0\lt 20\) \(2 x+5 y=80\) \(0 \leq 80\) \(2 x+5 y \leq 80\) So, the option (c) is right.
CG PET-2005
Linear Inequalities and Linear Programming
88561
The maximum value of \(Z=4 x+y\) subject to the constraints, \(x+y \leq 50,3 x+y \leq 90, x \geq 0, y\) \(\geq 0\) is
1 40
2 130
3 120
4 50
Explanation:
(C) : Given, \(\begin{align*} & l_{1}=\mathrm{x}+\mathrm{y}=50 \tag{i}\\ & l_{2}: 3 \mathrm{x}+\mathrm{y}=90 \tag{ii} \end{align*}\) \(\mathrm{Z}_{\max }=4 \mathrm{x}+\mathrm{y}\) \(\left.Z\right|_{(0,0)}=0 ;\left.Z\right|_{(0,50)}=50\) \(|Z|_{(20,30)}=80+30=110\) \(\left.\mathrm{Z}\right|_{(30,0)}=120\) \(\therefore\) Maximum value of \(\mathrm{Z}=120\)
AMU-2010
Linear Inequalities and Linear Programming
88563
The minimum value of the expression \(\frac{3 b+4 c}{a}+\frac{4 c+a}{3 b}+\frac{a+3 b}{4 c}(a, b, c\) are \(+v e)\) is
1 1
2 4
3 6
4 8
Explanation:
(C) : Given, The expression \(\frac{3 b+4 c}{a}+\frac{4 c+a}{3 b}+\frac{a+3 b}{4 c},(a, b, c\) are \(+v e)\) \(\frac{3 b}{a}+\frac{4 c}{a}+\frac{4 c}{3 b}+\frac{a}{3 b}+\frac{a}{4 c}+\frac{3 b}{4 c}\) \(\frac{3 b}{a}+\frac{a}{3 b}+\frac{4 c}{a}+\frac{a}{4 c}+\frac{4 c}{3 b}+\frac{3 b}{4 c}\) by \(\left(a+\frac{1}{a}\right) \geq 2\) for all value of \(a>0\) \(\left(\frac{3 b}{a}+\frac{a}{3 b}\right)+\left(\frac{4 c}{a}+\frac{a}{4 c}\right)+\left(\frac{4 c}{3 b}+\frac{3 b}{4 c}\right) \geq 2+2+2\) \(\left(\frac{3 b}{a}+\frac{a}{3 b}\right)+\left(\frac{4 c}{a}+\frac{a}{4 c}\right)+\left(\frac{4 c}{3 b}+\frac{3 b}{4 c}\right) \geq 6\)
AMU-2005
Linear Inequalities and Linear Programming
88564
The solution set of the inequality \(\log _{\sin (\pi / 3)}\left(\mathrm{x}^{2}-3 \mathrm{x}+2\right) \geq 2\) is
1 \(2 x+5 y \geq 80, x+y \leq 20, x \geq 0, y \leq 0\)
2 \(2 x+5 y \geq 80, x+y \geq 20, x \geq 0, y \geq 0\)
3 \(2 x+5 y \leq 80, x+y \leq 20, x \geq 0, y \geq 0\)
4 \(2 x+5 y \leq 80, x+y \leq 20, x \leq 0, y \leq 0\)
Explanation:
(C) : Given, From above figure it is clear that- \(x, y \geq 0\) \(x+y=20\) \(x+y \leq 20\) \((0,0)\) \(0\lt 20\) \(2 x+5 y=80\) \(0 \leq 80\) \(2 x+5 y \leq 80\) So, the option (c) is right.
CG PET-2005
Linear Inequalities and Linear Programming
88561
The maximum value of \(Z=4 x+y\) subject to the constraints, \(x+y \leq 50,3 x+y \leq 90, x \geq 0, y\) \(\geq 0\) is
1 40
2 130
3 120
4 50
Explanation:
(C) : Given, \(\begin{align*} & l_{1}=\mathrm{x}+\mathrm{y}=50 \tag{i}\\ & l_{2}: 3 \mathrm{x}+\mathrm{y}=90 \tag{ii} \end{align*}\) \(\mathrm{Z}_{\max }=4 \mathrm{x}+\mathrm{y}\) \(\left.Z\right|_{(0,0)}=0 ;\left.Z\right|_{(0,50)}=50\) \(|Z|_{(20,30)}=80+30=110\) \(\left.\mathrm{Z}\right|_{(30,0)}=120\) \(\therefore\) Maximum value of \(\mathrm{Z}=120\)
AMU-2010
Linear Inequalities and Linear Programming
88563
The minimum value of the expression \(\frac{3 b+4 c}{a}+\frac{4 c+a}{3 b}+\frac{a+3 b}{4 c}(a, b, c\) are \(+v e)\) is
1 1
2 4
3 6
4 8
Explanation:
(C) : Given, The expression \(\frac{3 b+4 c}{a}+\frac{4 c+a}{3 b}+\frac{a+3 b}{4 c},(a, b, c\) are \(+v e)\) \(\frac{3 b}{a}+\frac{4 c}{a}+\frac{4 c}{3 b}+\frac{a}{3 b}+\frac{a}{4 c}+\frac{3 b}{4 c}\) \(\frac{3 b}{a}+\frac{a}{3 b}+\frac{4 c}{a}+\frac{a}{4 c}+\frac{4 c}{3 b}+\frac{3 b}{4 c}\) by \(\left(a+\frac{1}{a}\right) \geq 2\) for all value of \(a>0\) \(\left(\frac{3 b}{a}+\frac{a}{3 b}\right)+\left(\frac{4 c}{a}+\frac{a}{4 c}\right)+\left(\frac{4 c}{3 b}+\frac{3 b}{4 c}\right) \geq 2+2+2\) \(\left(\frac{3 b}{a}+\frac{a}{3 b}\right)+\left(\frac{4 c}{a}+\frac{a}{4 c}\right)+\left(\frac{4 c}{3 b}+\frac{3 b}{4 c}\right) \geq 6\)
AMU-2005
Linear Inequalities and Linear Programming
88564
The solution set of the inequality \(\log _{\sin (\pi / 3)}\left(\mathrm{x}^{2}-3 \mathrm{x}+2\right) \geq 2\) is
1 \(2 x+5 y \geq 80, x+y \leq 20, x \geq 0, y \leq 0\)
2 \(2 x+5 y \geq 80, x+y \geq 20, x \geq 0, y \geq 0\)
3 \(2 x+5 y \leq 80, x+y \leq 20, x \geq 0, y \geq 0\)
4 \(2 x+5 y \leq 80, x+y \leq 20, x \leq 0, y \leq 0\)
Explanation:
(C) : Given, From above figure it is clear that- \(x, y \geq 0\) \(x+y=20\) \(x+y \leq 20\) \((0,0)\) \(0\lt 20\) \(2 x+5 y=80\) \(0 \leq 80\) \(2 x+5 y \leq 80\) So, the option (c) is right.
CG PET-2005
Linear Inequalities and Linear Programming
88561
The maximum value of \(Z=4 x+y\) subject to the constraints, \(x+y \leq 50,3 x+y \leq 90, x \geq 0, y\) \(\geq 0\) is
1 40
2 130
3 120
4 50
Explanation:
(C) : Given, \(\begin{align*} & l_{1}=\mathrm{x}+\mathrm{y}=50 \tag{i}\\ & l_{2}: 3 \mathrm{x}+\mathrm{y}=90 \tag{ii} \end{align*}\) \(\mathrm{Z}_{\max }=4 \mathrm{x}+\mathrm{y}\) \(\left.Z\right|_{(0,0)}=0 ;\left.Z\right|_{(0,50)}=50\) \(|Z|_{(20,30)}=80+30=110\) \(\left.\mathrm{Z}\right|_{(30,0)}=120\) \(\therefore\) Maximum value of \(\mathrm{Z}=120\)
AMU-2010
Linear Inequalities and Linear Programming
88563
The minimum value of the expression \(\frac{3 b+4 c}{a}+\frac{4 c+a}{3 b}+\frac{a+3 b}{4 c}(a, b, c\) are \(+v e)\) is
1 1
2 4
3 6
4 8
Explanation:
(C) : Given, The expression \(\frac{3 b+4 c}{a}+\frac{4 c+a}{3 b}+\frac{a+3 b}{4 c},(a, b, c\) are \(+v e)\) \(\frac{3 b}{a}+\frac{4 c}{a}+\frac{4 c}{3 b}+\frac{a}{3 b}+\frac{a}{4 c}+\frac{3 b}{4 c}\) \(\frac{3 b}{a}+\frac{a}{3 b}+\frac{4 c}{a}+\frac{a}{4 c}+\frac{4 c}{3 b}+\frac{3 b}{4 c}\) by \(\left(a+\frac{1}{a}\right) \geq 2\) for all value of \(a>0\) \(\left(\frac{3 b}{a}+\frac{a}{3 b}\right)+\left(\frac{4 c}{a}+\frac{a}{4 c}\right)+\left(\frac{4 c}{3 b}+\frac{3 b}{4 c}\right) \geq 2+2+2\) \(\left(\frac{3 b}{a}+\frac{a}{3 b}\right)+\left(\frac{4 c}{a}+\frac{a}{4 c}\right)+\left(\frac{4 c}{3 b}+\frac{3 b}{4 c}\right) \geq 6\)
AMU-2005
Linear Inequalities and Linear Programming
88564
The solution set of the inequality \(\log _{\sin (\pi / 3)}\left(\mathrm{x}^{2}-3 \mathrm{x}+2\right) \geq 2\) is
1 \(2 x+5 y \geq 80, x+y \leq 20, x \geq 0, y \leq 0\)
2 \(2 x+5 y \geq 80, x+y \geq 20, x \geq 0, y \geq 0\)
3 \(2 x+5 y \leq 80, x+y \leq 20, x \geq 0, y \geq 0\)
4 \(2 x+5 y \leq 80, x+y \leq 20, x \leq 0, y \leq 0\)
Explanation:
(C) : Given, From above figure it is clear that- \(x, y \geq 0\) \(x+y=20\) \(x+y \leq 20\) \((0,0)\) \(0\lt 20\) \(2 x+5 y=80\) \(0 \leq 80\) \(2 x+5 y \leq 80\) So, the option (c) is right.
CG PET-2005
Linear Inequalities and Linear Programming
88561
The maximum value of \(Z=4 x+y\) subject to the constraints, \(x+y \leq 50,3 x+y \leq 90, x \geq 0, y\) \(\geq 0\) is
1 40
2 130
3 120
4 50
Explanation:
(C) : Given, \(\begin{align*} & l_{1}=\mathrm{x}+\mathrm{y}=50 \tag{i}\\ & l_{2}: 3 \mathrm{x}+\mathrm{y}=90 \tag{ii} \end{align*}\) \(\mathrm{Z}_{\max }=4 \mathrm{x}+\mathrm{y}\) \(\left.Z\right|_{(0,0)}=0 ;\left.Z\right|_{(0,50)}=50\) \(|Z|_{(20,30)}=80+30=110\) \(\left.\mathrm{Z}\right|_{(30,0)}=120\) \(\therefore\) Maximum value of \(\mathrm{Z}=120\)
AMU-2010
Linear Inequalities and Linear Programming
88563
The minimum value of the expression \(\frac{3 b+4 c}{a}+\frac{4 c+a}{3 b}+\frac{a+3 b}{4 c}(a, b, c\) are \(+v e)\) is
1 1
2 4
3 6
4 8
Explanation:
(C) : Given, The expression \(\frac{3 b+4 c}{a}+\frac{4 c+a}{3 b}+\frac{a+3 b}{4 c},(a, b, c\) are \(+v e)\) \(\frac{3 b}{a}+\frac{4 c}{a}+\frac{4 c}{3 b}+\frac{a}{3 b}+\frac{a}{4 c}+\frac{3 b}{4 c}\) \(\frac{3 b}{a}+\frac{a}{3 b}+\frac{4 c}{a}+\frac{a}{4 c}+\frac{4 c}{3 b}+\frac{3 b}{4 c}\) by \(\left(a+\frac{1}{a}\right) \geq 2\) for all value of \(a>0\) \(\left(\frac{3 b}{a}+\frac{a}{3 b}\right)+\left(\frac{4 c}{a}+\frac{a}{4 c}\right)+\left(\frac{4 c}{3 b}+\frac{3 b}{4 c}\right) \geq 2+2+2\) \(\left(\frac{3 b}{a}+\frac{a}{3 b}\right)+\left(\frac{4 c}{a}+\frac{a}{4 c}\right)+\left(\frac{4 c}{3 b}+\frac{3 b}{4 c}\right) \geq 6\)
AMU-2005
Linear Inequalities and Linear Programming
88564
The solution set of the inequality \(\log _{\sin (\pi / 3)}\left(\mathrm{x}^{2}-3 \mathrm{x}+2\right) \geq 2\) is
