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Explain solution for RD Sharma Class 12 Chapter 29 Linear Programming Exercise Multiple Choice Question Question 17 maths textbook solution.

Answers (1)

Answer : (d) $q=3p$

Hint:

Find $z$ by the given corner points

Given:

Linear inequalities,

$\\2 x+y \leq 10, x+3 y \leq 15, x, y \geq 0$ are $(0,0),(5,0),(3,4)$ and $(0,5)$

Let $z=p x+q y$ where, $p, q>0$

Solution :

Let's find $z=p x+q y$ by the given corner points

Corner Points	Value of $z$
$(0,0)$	$0$
$(5,0)$	$5p$
$(3,4)$	$3p+4q$
$(0,5)$	$5q$

Now comparing corner points $(3,4)$ and $(0,5)$

$\text {Value on }(3,4)=\text {value on}(0,5)$

$3\text{p}+4\text{q}=5\text{q}$

$3\text{p}=\text{q}$

So, the correct option is (d)

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