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Please Solve RD Sharma Class 12 Chapter 29 Linear Programming Exercise 29.4 Question 3 Maths Textbook Solution.

Answers (1)

Answer:

A should work for 5 days and B should for 3 days.

Hint:

Let tailor A and B work for x and y days respectively.

Given:

Tailor A and B earn Rs15 and Rs20 respectively.

Solution:

Min $z =15x+20y$

Since tailor A and B stitch 6 and 10 shirts respectively in a day. But it is desired to produce 60 shirts at least. So,

$6x+10y\geq 60$

$\Rightarrow 3x+5y\geq 30$ (First constraint)

Since tailor A and B stitch 4pants per day but it is desired to produce at least 32 pants so

$4x+4y\geq 32$

$\Rightarrow x+y\geq 8$ (Second constraint)

Hence the required LPP .

Min $z =15x+20y$

Subject to constraints

$3x+5y\geq 30$

$x+y\geq 8$

$x,y\geq 0$ Since x and y not be less than zero.

The corresponding equation is

Point P(5,3) obtain by solving (i) and (ii)

Unbounded shaded region $A_{1}PB_{2}$ represents feasible region with corner points $A_{1}(10,0), P(5,3), B_{2}(0,8)$

Points	$z=15x+20y$
$A_{1}(10,0)$	$150$
$P\left ( 5,3 \right )$	$135$
$B_{2}\left ( 0,8 \right )$	$160$

Min z=135 at x=5 and y=3

Tailor A should work for 5 days and B should for 3 days.

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