SYSE 515 6.3 Addressing Complexity

There are many things that I learned this week and I would like to use this opportunity to review the simplex method (maximization with problem constraints) that I studied with an example question. 

There can be several methods to solve these kind of questions including the traditional ways of solving the problems by hand with equations and graphs. I find this way is also quite useful when approaching the problem.

I have attached my note that I made while I was studying the problem and solution. Studying the question with the handwritten solution greatly helped me to understand the concept of the simplex method.







Question

Suppose a company manufactures different electronic components for computers. Component A requires 2 hours of fabrication and 1 hour of assembly; Component B requires 3 hours of fabrication and 1 hour of assembly; and component C requires 2 hours of fabrication and 2 hours of assembly.

The company has up to 1000 labor-hours for fabrication and 800 labor hours of assembly time each week. If the profit on each component A, B and C is $7, $8, $10 respectively, how many of each should be produced to maximize profit?











References:


patrickJMT. (2010, August 16). The Simplex Method - Finding a Maximum / Word Problem Example, Part 1 of 5 [Video]. YouTube. https://www.youtube.com/watch?v=gRgsT9BB5-8&list=PLIs7IgTI76WzkWuDcMM9IhXj3SkiAZeMn


patrickJMT. (2010b, August 16). The Simplex Method - Finding a Maximum / Word Problem Example, Part 2 of 5 [Video]. YouTube. https://www.youtube.com/watch?v=yL7JByLlfrw&list=PLIs7IgTI76WzkWuDcMM9IhXj3SkiAZeMn&index=2


patrickJMT. (2010c, August 16). The Simplex Method - Finding a Maximum / Word Problem Example, Part 3 of 5 [Video]. YouTube. https://www.youtube.com/watch?v=vVzjXpwW2xI&list=PLIs7IgTI76WzkWuDcMM9IhXj3SkiAZeMn&index=3


patrickJMT. (2010d, August 16). The Simplex Method - Finding a Maximum / Word Problem Example, Part 4 of 5 [Video]. YouTube. https://www.youtube.com/watch?v=lPm46c1pfvQ&list=PLIs7IgTI76WzkWuDcMM9IhXj3SkiAZeMn&index=4


patrickJMT. (2010e, August 16). The Simplex Method - Finding a Maximum / Word Problem Example, Part 5 of 5 [Video]. YouTube. https://www.youtube.com/watch?v=WeK4JjNLSgw&list=PLIs7IgTI76WzkWuDcMM9IhXj3SkiAZeMn&index=5


Simplex Method - an overview | ScienceDirect Topics. (n.d.). ScienceDirect. Retrieved September 20, 2020, from https://www.sciencedirect.com/topics/mathematics/simplex-method


Linear Programming Problems, Linear Programming Simplex Method. (n.d.). Civil Service India Your IAS Guide. Retrieved September 20, 2020, from https://www.civilserviceindia.com/subject/Management/notes/linear-programming.html

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