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How to solve Berlin Airlift Linear Optimization Problem
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How will you go about solving following problem in Smath Problem statement is as follows: Quote:On June 24, 1948, the former Soviet Union blocked all land and water routes through East Germany to Berlin. A gigantic airlift was organized using American and British planes to supply food, clothing and other supplies to more than 2 million people in West Berlin. The cargo capacity was 30,000 cubic feet for an American plane and 20,000 cubic feet for a British plane. To break the Soviet blockade, the Western Allies had to maximize cargo capacity, but were subject to the following restrictions: No more than 44 planes could be used. The larger American planes required 16 personnel per flight; double that of the requirement for the British planes. The total number of personnel available could not exceed 512. The cost of an American flight was $9000 and the cost of a British flight was $5000. The total weekly costs could note exceed $300,000. Find the number of American and British planes that were used to maximize cargo capacity. Based on this the author & using an online LP solver I have: http://prntscr.com/hpk4j5
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You can use the "simplex" package in Maxima (linear optimization) See page Examples> Maxima usage> Linear optimization in the interactive handbook. Example maxima linear optimization.sm (42kb) downloaded 23 time(s). |
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Originally Posted by: ioncube How will you go about solving following problem in Smath Maybe plot the problem 1rst ? Next solve solely with Smath, whereas Maxima is not component of stable 6179.
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Joined: 04/12/2017(UTC) Posts: 61 Was thanked: 2 time(s) in 2 post(s)
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Thanks for the answers Jean would you be kind enough to attach the .sm file too. For field engineers like us your math skills seems rather cryptic & is digested properly after 2/3 days of experimenting
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Originally Posted by: ioncube Thanks for the answers Jean would you be kind enough to attach the .sm file too. Here is + some extra stuff. Maybe there is way to draw an inscribed 3D ? Jean Solve GivenFind Critical Region Copy.sm (40kb) downloaded 27 time(s).
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Using Smath Studio with Maxima and the example of Martin Kraska. Metodo_Simplex.sm (53kb) downloaded 23 time(s).Best Regards Carlos
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Here is a small and simple Simplex algorithm without the use of the Maxima function. Small_Simplex_Algorithm.sm (17kb) downloaded 22 time(s).Best regards Carlos CAUTION: The algorithm is NOT TESTED, but it works well for this example. It is necessary to refine it so that it work in all cases. Edited by user 21 December 2017 22:13:26(UTC)
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1 user thanked CBG for this useful post.
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Thanks Carlos for the "Simplex algo"
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Rank: Advanced Member Groups: Registered
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Rank: Advanced Member Groups: Registered
Joined: 14/10/2015(UTC) Posts: 308
Was thanked: 77 time(s) in 58 post(s)
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Joined: 04/07/2015(UTC) Posts: 6,868 Was thanked: 980 time(s) in 808 post(s)
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Originally Posted by: CBG I'm sorry, I found a bug in the Simplex algorithm. That huge number in the program, can be replaced by ∞ [Smath machine number] RemToDo => check vs Mathcad First A[i ... badly indexed. Small_Simplex_Algorithm_Improved_2.sm (141kb) downloaded 27 time(s).
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1 user thanked Jean Giraud for this useful post.
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Thanks Jean, Now we just have to continue testing the Simplex algorithm, to identify possible faults.
regards
Carlos
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Originally Posted by: CBG Thanks Jean, Now we just have to continue testing the Simplex algorithm, to identify possible faults. I have tested only this one => 1/1 Mathcad 11 Gorgeous, hope for more good ! Jean Undocumented Copy.sm (26kb) downloaded 33 time(s).
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How to solve Berlin Airlift Linear Optimization Problem
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