1 Marks Question

Question 11 Mark

Show the feasible region of the constraints $3 x+5 y \leq 15, x \geq 0, y \geq 0$.

Answer

The corresponding equations $3 x+5 y=15$
$
\Rightarrow \quad \frac{x}{5}+\frac{y}{3}=1
$
It meets the $x$-axis at the point $(5,0)$ and $y$-axis $(0,3)$.

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Question 21 Mark

Show the feasible region of the constraints $2 x+y \leq 4$, $x \geq 0, y \geq 0$.

Answer

The corresponding equation is
$
\begin{aligned}
& \begin{aligned}
2 x+y & =4 \\
\Rightarrow & \\
\frac{x}{2}+\frac{y}{4} & =1
\end{aligned} \text { r }
\end{aligned}
$
It meets $x$-axis at the point $(2,0)$ and $y$-axis at the point $(0,4)$. Since the inequality is satisfied by the origin, therefore the solution region will be towards the origin.

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Question 31 Mark

Show the feasible region under the constraints $x+y \leq$ $4, x \geq 0, y \geq 0$.

Answer

Changing the given inequation into equation.
$
\Rightarrow \quad \begin{aligned}
x+y & =4 \\
y & =-x+4 \\
x=0, y & =0
\end{aligned}
$
Drawing the lines of these equation it is obvious that the feasible region OAB (shaded) is bounded.

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Question 41 Mark

Define linear objective function.

Answer

The linear function $Z =a x+b y$, where $a, b$ are constants, of which the maximization on minimization is to be done, is called a linear objective function. For example, $Z=500 x+125 y$ is a linear objective function. Here $x$ and $y$ are called decision variables.

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Question 51 Mark

What are optimal feasible problems?

Answer

The problems determined by set of inequalities under fixed constraints which maximises or minimises the linear function in two variables (for example, two variables $x$ and $y$ ) are called optimal feasible problems.

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