CS 312, section 003

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April 04, 2005

Linear programming problem (due 4/13)

Here is the problem to solve with your linear programming project. The project is due the last day of classes. There will be no late days. The project is to turn this problem into a linear programming problem and then solve it with your simplex solver. You are free to use any input format you like and you are free to just hard-code the input right into your program if you like. This is the only problem your program will be tested on (but we will look at your source code to make sure your program isn't just "wait 2 seconds then return the solution").

You are the operations director for a processing plant at a large mine. Your job is to devise a program, or plan, for the plant that maximizes profits while staying within the resource budget. The plant produces four major resources: copper, gold, silver and platinum.

In a given week, the mine produces 2,000 tons of ore that must be processed into some combination of the four major resources. A ton of ore contains 10 ounces of copper, 2 ounces of gold, 3 ounces of silver and 1 ounce of platinum. You many only extract one resource from each unit of ore processed.

Processing the ore requires power, water, labor and use of one of the three processing lines. Producing each of the resources requires different amounts of processing resources. One ounce of copper requires 30 kW hours, 1,000 gallons of water, 50 hours of labor and 4 hours of processing time on a processing line. One ounce of gold requires 15 kW hours, 6,000 gallons of water, 20 hours of labor and 6 hours of processing time on a processing line. One ounce of silver requires 19 kW hours, 4,100 gallons of water, 21 hours of labor and 19 hours of processing time on a processing line. One ounce of platinum requires 12 kW hours, 9,100 gallons of water, 10 hours of labor and 30 hours of processing time on a processing line.

There is only a limited amount of power, water, labor and processsing line time available. In a given week, you may use 1,000 kW hours of power, 1,000,000 gallons of water, 640 hours of laber and you can run the processing lines 24 hours a day for 7 days a week for a total of 504 hours.

Finally, each ounce of finished resource has an associated profit. An ounce of copper is worth $10.20, an ounce of gold is worth $422.30 dollars, an ounce of silver is worth $6.91 and an ounce of platinum is worth $853.00.

Posted by jones at April 4, 2005 10:29 AM

Comments

Posted by: Matt Doyle at April 12, 2005 11:28 AM

Posted by: Mike Jones at April 12, 2005 01:21 PM

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