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?_______________