Question

Consider the following statements
Statement I The solution set of the system of inequalities $5x+4y\le 20,x\ge 1,y\ge 2$ is

Statement II The solution set of the inequalities $3x+4y\le 60,x+3y\le 30,x\ge 0,y\ge 0$ is

Choose the correct option.

• A. Statement $I$ is true
• B. Statement II is true
• C. Both are true
• D. Both are false

Answer 1

Answer: (B)

I. The given system of inequalites
$5x+4y\le 20$...(i)
$x\ge 1$ ...(ii)
$y\ge 2$ ...(iii)
Step I Consider the inequations as strict equations i.e., $5x+4y=20$
$x=1,y=2$
Step II Find the points on the $X$-axis and $Y$-axis for $5x+4y=20$

Step III Plot the graph using the above tables.
(i) For $5x+4y=20$ use the above table.
(ii) Graph of $x=1$ will be line parallel to $Y$-axis, intersecting the $X$-axis at 1.
(iii) Graph of $y=2$ will be a line parallel to $X$-axis, intersecting the $Y$-axis at 2 .

Step IV Take a point $(0,0)$ and put it in the given inequations (i), (ii) and (iii),
$0+0\le 20\text{ (true) }$
$0\ge 1\text{ (false) }$
$0\ge 2\text{ (false) }$
Thus, common shaded region shows the solutions of the inequalities.
II. The given system of inequalities
$3x+4y\le 60$...(i)
$x+3y\le 30$...(ii)
$x\ge 0$...(iii)
$y\ge 0$...(iv)
Step I Consider the inequations as strict equations
$\text{ i.e., }3x+4y=60,x+3y=30$
$x=0,y=0$
Step II Find the points on the $X$-axis and $Y$-axis for

Step III Plot the graph using the above tables.
(i) For $3x+4y=60$ and $x+3y=30$ use the above tables.
(ii) Graph of $x=0$, will be $Y$-axis.
(iii) Graph of $y=0$, will be $X$-axis
Step IV Take a point $(0,0)$ and put it in inequations (i) and (ii),
$0+0\le 60\text{ (true) }$
So, the shaded region will be towards origin. and
$0+0\le 30$(true)
So, the shaded region will be towards origin.

And point $(1,0)$ in inequation (iii),
$1\ge 0$ (true)
So, the shaded region will be towards origin.
Point $(0,1)$ in inequation (iv),
$1\ge 0$(true)
So, the shaded region will be towards origin.
Thus, common shaded region shows the solution of the inequalities.