The Grand Valley Company, run by the J. Motwani family, produces two products: bed mattresses and box springs. A prior contract requires that the firm produce at least 30 mattresses or box springs, in any combination, per week. In addition, union labour agreements demand that stitching machines be kept running at least 40 hours per week, which is one production period. Each box spring takes 2 hours of stitching time, while each mattress takes 1 hour on the machine. Each mattress produced cost $20 and each box spring costs $24. Formulate this problem as a linear programming problem.