A textile can make pants and sshirts. it can sell pants for 6$ profit per pairs and shirts for 3$ per shirts. the manufacturing process consists of a knitting machine and the cutting and sewing department. each pair of pants takes 10 mins to machine knit, 30 mins to cut and sew, and 30$ in materials costs. each shirt takes 20 min to knit. 20 minutes to cut and sew, and 31$ in materials costs. the knitting machine provides 125 hours per week of service time, the cutting and sewing department has 180 labor hours available, and the materials costs are covered from 12600$ weekly materials budget.
what is the optimum mix of pants and shirts for the textile mill to manufacture each week?