Smith’s, a Niagara, New York, clothing manufacturer that produces men’s shirts and pajamas, has two primary resources available: sewing-machine time (in the sewing department)

and cutting-machine time (in the cutting department). Over the next month, owner Barbara Smith can schedule up to 280 hours of work on sewing machines and up to 450 hours of work on cutting machines. Each shirt produced requires 1.00 hour of sewing time and 1.50 hours of cutting time.

Producing each pair of pajamas requires .75 hours of sewing time and 2 hours of cutting time.

To express the LP constraints for this problem mathematically, we let:

X1 = number of shirts produced X2 = number of pajamas produced