Optimizing Mineral Extraction: How Can Linear Programming Help?

AI Thread Summary
Blacktop refining seeks to optimize mineral extraction from two ore types using linear programming. Ore type 1 contains 20% copper, 20% zinc, and 15% magnesium, costing $90 per ton, while ore type 2 contains 30% copper, 25% zinc, and 10% magnesium at $120 per ton. The goal is to acquire enough ore to yield at least 8 tons of copper, 6 tons of zinc, and 5 tons of magnesium at the lowest cost. Forum participants emphasize the importance of attempting the problem before seeking help and express frustration over lack of effort from the original poster. The discussion highlights the need for a structured approach to formulating the linear programming model and identifying the feasible region for optimal solutions.
ama111
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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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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.
 

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