The Our-Bags-Don't-Break (OBDB) plastic bag company manufactures three plastic refuse bags for home use: a 20-gallon garbage bag, a 30-gallon garbage bag, and a 33-gallon leaf- and-grass bag. Using purchased plastic material, three operations are required to produce each end product: cutting, sealing, and packaging. The production time required to process each type of bag in every operation and the maximum production time available for each operation are shown (note that the production time figures in this table are per box of each type of bag).
|
Type of Bag
20 gallons
|
Cutting
2
|
Sealing
2
|
Packaging
3
|
|
30 gallons
|
3
|
2
|
4
|
|
33 gallons
|
3
|
3
|
5
|
|
Time available
|
2 hours
|
3 hours
|
4 hours
|
If OBDB's profit contribution is $0.10 for each box of 20-gallon bags produced, $0.15 for each box of 30-gallon bags, and $0.20 for each box of 33-gallon bags, what is the optimal product mix?