Question
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
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 20 oz 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 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 18lbs. of plastic resins to produce while 16 oz cups require 14 lbs. per case. The daily supply of plastic resins is limited 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.
Make system of linear equations that model this situation.
Let x =_____________
Let y =_____________
Number of cases that can be made in 8 hours:_______________
Maximum Amount of plastic resin used per day:______________
Number of 16 oz vs 20 oz cups made:____________
Use either substitution or elimination to solve the system of equation:
What is the solution to this system?______________
What does this solution represent?_______________
Graph the system of equations:
Find an equation to represent the Profit: P=__________________
What is the maximum profit that can be made given the parameters of this system:____________
Currently, the smoothie company purchases three times as many 16 oz cups to 20 oz cups, however, they said in the near future they would like to order four times as many 16 oz cups to 20 oz cups.
How many of each type of cup should be made if the smoothie company changes their order?_________________
What would the profit be for this new situation?_______________
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