Question

Two tailors, $A$ and $B$, earn Rs $300$ and Rs $400$ per day respectively. $A$ can stitch $6$ shirts and $4$ pairs of trousers while $B$ can stitch $10$ shirts and $4$ pairs of trousers perday. To find how many days should each of them work if it is desired to produce at least $60$ shirts and $32$ pairs of trousers at a minimum labour cost, formulate this as an LPP.

Answer 1

	Tailor $A$	Tailor $B$	Minimum Total No.
No. of shirts	$6$	$10$	$60$
No. of pair of trousers	$4$	$4$	$32$
Wage	Rs $300$/day	Rs $400$/day

Let $A$ and $B$ work for $x$ and $y$ days respectively to produce required consignment.
$\therefore x\ge 0,y\ge 0$
Subject to constraints:
Minimum no of shirt = $60$
$\Rightarrow 6x+10y\ge 60or3x+5y\ge 30$
Minimum no of trouser = $32$
$\Rightarrow 4x+4y\ge 32orx+y\ge 8$

$\therefore$ Formation of LPP according to the given statement is as :
$Z$ is the total labour cost
The given L.P problem reduces to:
Minimize $Z=300x+400y$
Subjected to:
$x\ge 0,y\ge 0,3x+5y\ge 30andx+y\ge 8$