Gerard.inc. is one of the leading producers of dairy exports. The company has 2 variants of superior milk, namely mocha and green tea. Based on historical data, the R&D team has found that the advantage per liter for each milk variant follows the following equation: πmocha = $45 - 0.9x and πgreen-tea = $65 - 1.7y Where x is the number of liters of mocha milk produced and y is the number of liters of green tea milk produced. It takes 2 hours to produce 1 liter of mocha milk and 5 hours to produce 1 liter of green tea milk. With the current number of workers, companies have a total of 40 hours of work in a day, and everything should be used to make both variants. The company wants to know the optimal amount of milk to be produced. a. How many liters of mocha milk and green tea should the company produce? b. What is the optimal objective function value based on your calculations? c. What is the lagrange multiplier value and what does it mean?
Gerard.inc. is one of the leading producers of dairy exports. The company has 2 variants of superior milk, namely mocha and green tea. Based on historical data, the R&D team has found that the advantage per liter for each milk variant follows the following equation:
πmocha = $45 - 0.9x and πgreen-tea = $65 - 1.7y
Where x is the number of liters of mocha milk produced and y is the number of liters of green tea milk produced. It takes 2 hours to produce 1 liter of mocha milk and 5 hours to produce 1 liter of green tea milk. With the current number of workers, companies have a total of 40 hours of work in a day, and everything should be used to make both variants. The company wants to know the optimal amount of milk to be produced.
a. How many liters of mocha milk and green tea should the company produce?
b. What is the optimal objective function value based on your calculations?
c. What is the lagrange multiplier value and what does it mean?
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