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 $x\&y$ 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:
$x\ge 0,y\ge 0,3x+5y\ge 30\text{and}x+y\ge 8$