A local family-owned plastic cup manufacturer wants to optimize their production mix in order to maximize their profit. They produce 2 sizes of plastic cups for a chain of stores selling smoothies; 16 oz and 20oz cups. Currently, the smoothie company purchases three times as many 16 oz cups to 20 oz cups. The profit on a case of 20 oz plastic cups is $20 while the profit on a case of 16 oz plastic cups is $25.
The cups are manufactured with a machine called a plastic extruder which feeds on plastic resins. Each case of 20 oz cups requires 18 lbs. of plastic resins to produce while 16 oz plastic cups require 14 lbs. per case. The daily supply of plastic resins is limited to at most 1800 pounds.
About 15 cases of either product can be produced per hour. At the moment, the family wants to limit their workday to 8 hours.