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 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.

Let A work forxdays and B work forydays.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 write6x+10y≥60 ... (2)4x+4y≥32 ... (1)We therefore need to minimize the function300x+400ysubject to the conditions as mentioned in equations (1) and (2) above.Solving both equations, we getx=5andy=3A and B should work for5and3days to produce60shirts and32pairs of trousers.