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Provide Solution For R.D. Sharma Maths Class 12 Chapter 29 Linear Programming Exercise 29.3 Question 8 Maths Textbook Solution.

Answers (1)

Answer: ?72

Hint: Draw a graph

Given: Mixture A costs ? 8 per Kg and B costs ?12 per Kg

Solution: Let ‘x’ be the quantity of A mixture and ‘y’ be the quantity of B mixture

Minimize,

$8x + 12y =z$

sub to contraits

$\begin{gathered} 60 x+30 y \geq 240 \Rightarrow 2 x+y \geq 8 \\ \end{gathered}$

$\begin{gathered} 30 x+60 y \geq 300 \Rightarrow x+2 y \geq 10 \\ \end{gathered}$

$\begin{gathered} 30 x+180 y \geq 540 \Rightarrow x+6 y \geq 18 \\ \end{gathered}$

$\begin{gathered} x \geq 0, y \geq 0 \end{gathered}$

Solving (i) & (ii), we get

$x=2,y=4$

Solving (ii) & (iii) we get

$x=6,y=2$

Points	Value of z
$\left ( 0,8 \right )$	$6$
$\left ( 2,4 \right )$	$72$
$\left ( 6,2 \right )$	$72$
$\left ( 18,0 \right )$	$144$

Minimum cost is ? 72.

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