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Need solution for RD sharma maths class 12 chapter 29 Linear Programming exercise Fill in the blanks question 9

Answers (1)

$Z_{min}=15$ at $\left ( \frac{5}{4},\frac{5}{4} \right )$

Hint:

Assume the feasible region

Given:

The maximum of the objective function $z=2x+10y$ for linear constraints $x-y\geq 0$ , $x-5y\leq -5$ , $x\geq 0$ , $y\geq 0$ is _____

Solution:

From the linear constraints

$x-y=0$

$x=y$ and

Again

$\begin{aligned} &x-5 y=-5 \\ &x-y=0 \end{aligned}$ [Subtracting the constraints]

________________

$\begin{gathered} -4 y=-5 \\ \end{gathered}$

$\therefore y=\frac{5}{4}$ and $x=\frac{5}{4}$

The required region will be the unbounded area with the vertex $\left ( \frac{5}{4} ,\frac{5}{4}\right )$ ,so

$Z_{min}=15$ at $\left ( \frac{5}{4},\frac{5}{4} \right )$

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