Two tailors P and Q earn \$150 and \$200 per day respectively. P can stitch 6 shirts and 4 trousers a day, while Q can stitch 10 shirts and 4 trousers a day. How many days should each work to produce at least 60 shirts and 32 trousers at minimum labour cost?
My solution: Let P works for x days and Q works for y days. The linear programming problem can be written as: $$ Min z= 150x+200y\\ subject \space to \ 6x+10y \geq 60 \\ 4x+4y \geq 32 \\ x\geq0 , y\geq0 $$ The grey portion is the feasible region