Optimizing Mineral Extraction: How Can Linear Programming Help?

In summary, Blacktop refining is looking to extract minerals from two different ore types in Montana. Ore type 1 contains 20% copper, 20% zinc, and 15% magnesium and costs 90$ per ton, while ore type 2 contains 30% copper, 25% zinc, and 10% magnesium and costs 120$ per ton. The company needs to buy enough ore to extract at least 8 tons of copper, 6 tons of zinc, and 5 tons of magnesium in the most cost-effective way.To help with this task, three steps need to be taken:1. Formulating a Linear Programming model to determine the optimal solution.2. Identifying the feasible region, which is
  • #1
ama111
2
0

Homework Statement


Blacktop refining extracts minerals from ore mined at two different sites in Montana. Each ton of ore type 1 contains 20% copper, 20% zinc, and 15% magnesium. Each ton of ore type 2 contains 30% copper, 25% zinc, and 10% magnesium. Ore type 1 costs 90$ per ton, while ore type 2 costs 120$ per ton. Blacktop would like to buy enough ore to extract alteast 8 tons of copper, 6 tons of zinc, and 5 tons of magnesium in the least costly manner.

Need help in the following tasks:
1. formulating an Linear Programming model
2. feasible region
3. finding optimal solution

any help would be very appreciated:)
 
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  • #2
Ama111, please read the forum rules before you post.
Not only have you not shown any attempt - have you even tried this yourself?
Then if you start bumping your thread after 90 minutes already, I don't feel inclined to help you at all. If you're in such a hurry, start your homework earlier.
 

1. What is Linear Programming?

Linear Programming is a mathematical optimization technique used to find the best possible solution to a problem, given a set of linear constraints and a linear objective function. It is commonly used in fields such as engineering, economics, and management to maximize profits, minimize costs, or achieve other objectives.

2. What are the basic components of a Linear Programming problem?

The basic components of a Linear Programming problem include decision variables, objective function, constraints, and feasible region. Decision variables represent the quantities that need to be determined, the objective function defines the goal to be achieved, constraints limit the values that the decision variables can take, and the feasible region is the set of all possible solutions that satisfy the constraints.

3. What are the main assumptions of Linear Programming?

The main assumptions of Linear Programming include linearity, proportionality, additivity, divisibility, and certainty. Linearity means that the objective function and constraints must be linear functions of the decision variables. Proportionality means that the objective function and constraints must be directly proportional to the decision variables. Additivity means that the total contribution of all decision variables must be equal to the total contribution of their individual parts. Divisibility means that decision variables can take any non-negative value. Certainty means that all parameters and variables are known with certainty.

4. What are the different methods for solving Linear Programming problems?

The most commonly used methods for solving Linear Programming problems include the graphical method, the simplex method, and the interior point method. The graphical method is used for problems with two decision variables and can provide a quick and visual solution. The simplex method is a more general method and can handle problems with any number of decision variables. The interior point method is an advanced method that is more efficient for large and complex problems.

5. What are some real-world applications of Linear Programming?

Linear Programming has various real-world applications, such as production planning, inventory management, resource allocation, transportation planning, and financial planning. It is also commonly used in industries like agriculture, manufacturing, transportation, and finance to optimize production processes, minimize costs, and maximize profits. Additionally, Linear Programming is used in healthcare to optimize hospital operations and in sports to create optimal team lineups.

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