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 per day. To find how many days should each of them work and 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 and find the number of days $A$ and $B$ worked.

Answer 1

Let A work for $x$ days and B work for $y$ days.

Also, as per the given conditions on the number of shirts and trousers A can stitch per day and B can stitch per day, we can write

$6x+10y\ge 60...\left(2\right)$

$4x+4y\ge 32...\left(1\right)$

We therefore need to minimize the function $300x+400y$ subject to the conditions as mentioned in equations (1) and (2) above.

Solving both equations, we get

$x=5$ and $y=3$

A and B should work for $5$ and $3$ days to produce $60$ shirts and $32$ pairs of trousers.