A Simple Linear Programming Example: Equipment Bags
Our firm makes equipment bags for professional camera equipment. We have
two models: regular and deluxe. We have a prior pricing agreement with
our distributor, who is willing to buy as much of each kind of bag as we
could conceivably make.
There are four steps in making a bag:
Each regular bag requires 7/10 hour in cutting and dyeing, 1/2 hour in
sewing, 1 hour in finishing, and 1/10 hour in inspection and packing. On
the other hand, each deluxe bag needs 1 hour in cutting and dyeing, 5/6
hour in sewing, 2/3 hour in finishing, and 1/4 hour in inspection and packing.
The profit obtained for each regular bag is $10, while that for each
deluxe bag is $9.
Cutting and dyeing the material
Inspection and packaging
Finally, the director of manufacturing estimates that 630 hours for
cutting and dyeing, 600 hours for sewing, 708 hours for finishing, and
135 hours for inspection and packing will be available for manufacturing
the bags during the next production cycle.
In order to maximize the profit for the company, how many bags of each
type should we manufacture?