A company is dedicated to the production of different vegetable-flavored milks. Currently the company produces two types of milk: almond and coconut, which it sells at $ 5,000 and $ 2,000 / liter respectively. Milk production is subject to the use of machine hours in the production plant and of water as a fundamental resource. It takes 1 machine-hour and 2 liters of water to produce 1 liter of almond milk, while it takes 3 machine-hours and 1 liter of water to produce 1 liter of coconut milk. The company currently has 100 machine-hours and 50 liters of water to make the milk, and it is also required to make at least 30 liters of milk in total. 1. Set up the linear programming model in standard format. 2. Determine all the basic solutions to the problem. Identify which ones are feasible and which ones are not. Analyze what happens graphically. 3. Determine an initial feasible basic solution using phase I. In each iteration, write the resulting model in dictionary format and analyze what happens graphically. 4. Determine the optimal solution to the problem using phase II. In each iteration, write the resulting model in dictionary format and analyze what happens graphically.
A company is dedicated to the production of different vegetable-flavored milks. Currently the company produces two types of milk: almond and coconut, which it sells at $ 5,000 and $ 2,000 / liter respectively. Milk production is subject to the use of machine hours in the production plant and of water as a fundamental resource. It takes 1 machine-hour and 2 liters of water to produce 1 liter of almond milk, while it takes 3 machine-hours and 1 liter of water to produce 1 liter of coconut milk. The company currently has 100 machine-hours and 50 liters of water to make the milk, and it is also required to make at least 30 liters of milk in total.
1. Set up the linear programming model in standard format.
2. Determine all the basic solutions to the problem. Identify which ones are feasible and which ones are not. Analyze what happens graphically.
3. Determine an initial feasible basic solution using phase I. In each iteration, write the resulting model in dictionary format and analyze what happens graphically.
4. Determine the optimal solution to the problem using phase II. In each iteration, write the resulting model in dictionary format and analyze what happens graphically.
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