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Linear Programming! Index of Activity!
Fred Mikkelsen's Blog |
November 7, 2007 2:15 PM
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I'm looking over my STATS to pick up any information that may be valuable in tuning my blog for my market -- enterprise application developers. Here are the hit rates on my blogs so far:
To make sense of this data, I employed linear programming and solved for simultaneous linear equations. Accounting for the number of hits over the time an entry has been published, I find the correlation of hits related to the punctuation involved in title. - has negative value, ! gets the most attention, follwed by ? and finally an apostrophy has the value of a letter.
This is a silly case of applying these algebraic techniques, but real-world examples of applying linear programming occur all the time.
I remember in high school learning linear programming where you would solve for variables and unknowns based on complex information that is given to you. Statisticians would use it to calculate the prediction of income of a household based on the number of appliances and chairs around the dinner table and things like that.
A more common form would allow you to make decisions based on the ROI and cost of different commodities.
Example: mixing spices in a factory to maximize yield
You want to mix the most profitable batch of a spice, and you have a few product sources to choose from. The Law requires that 97% of a spice would be free from weeds. The law prohibits you from purposely mixing contaminates into a spice, but you can mix batches of varying purity provided no sticks and stems and weeds are added directly.
You have a source of spice that is 99.5% pure for $1000 a ton, and another that is 93% pure in the same spice for $550 per ton, and you have a previous batch that is 98% pure and not selling in the warehouse, but it would cost $100 to transport back to the mixing plant per shipment of 1000 pounds. You must also adjust the mixture of two preservatives of up to 1% of volume that cost $30/pound and $50/pound provided the first is not used in a proportion less than 2:1 to the second. If your spice is 99% pure or more, you can use as little as 0.25% preservative. However, if it is 99% or less pure, you must use 0.5% preservative or more.Given these restrictions, what is the cheapest cost per pound?
I remember in High School, circa TRS-80-days, solving this type of problem is what computers were expected to be able to do. This was decision support. Where has this gone?
I've been searching around the internet looking for good implementations of linear programming and solving linear equations, and haven't found any. I find it interesting that software had not been developed to solve the problems in the way we were taught in high school to solve problems.
Two questions (or three). Do you know of a good linear programming package? Would you use a package like this?
Did you come to this blog entry because the title had extra punctuation?
version: 1.1
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