The Bus Pants Utilization

The Bus Pants Utilization is the 12th episode of the fourth season of The Big Bang Theory.

Plot Summary
Leonard has an idea to make an smartphone app to solve differential equations. But Sheldon quickly puts himself in charge of the team to build the app, but Leonard is able to recover his place as the Leader. After some time Sheldon is unsatisfied with Leonard's leadership and call for a vote to change the Leader, which result in Sheldon getting kicked out.

Expanded Plot
Sheldon, Howard and Raj are eating together in the Cafeteria when Leonard approaches them with an idea for a smartphone app that helps users solve Differential Equations. Leonard quickly recruits Howard and Raj and Sheldon who recruited himself. Leonard mentions they may make a little money of the app, Howard hope to building a place at over the garage to escape his mother with the money and Raj dreams of taking pretty girls on "Submarine Ride". When they get back home, Leonard tells that nobody else is currently making an app like theirs, in the presence of Penny, Sheldon is afraid Penny will steal Leonard's idea, he points out an "Unlikely but very plausible scenario" that Penny befriends the gang to steal a marketable idea from them, Penny points out that she hangs out with them partly because she receives free food. After Penny leaves, Sheldon quickly designates himself as the Leader of the group, when he lists himself as Chief Executive Officer, Chief Financial Officer, Chief Operating Officer, Chief Science Officer, Chairman Of the Board and Head of the Secret Santa Committee, meanwhile Leonard is only listed as Founder. After a little argument Leonard was able to regain his post as the Leader. Over time Sheldon continue to mock Leonard's leadership until he proposes a vote to change the Leadership, this results in him getting thrown off the team. Although Sheldon is off the team, Leonard is still fine with driving him to work, but that changes after Sheldon mocking Leonard's height and saying he has a "Big Napoleon Complex", Sheldon has to put on his Bus Pants and use the bus to go to work (presumably this is the origin of the title). Sheldon tries to persuade Howard and Raj to join his rivaling team and abandon Leonard with gifts, failing that Sheldon tries to hinder the team's progress by playing the Theremin, which results in him getting kicked out the apartment. Penny finds Sheldon playing it at the hallway and tells him about her idea for an app that help user find places on the internet to but shoes which Sheldon turns down, feeling sympathy for him she invites him for Hot Cocoa, he accepts with the remark "A disappointing drink for a disappointing day" a decision which she soon regret, Leonard agrees that he will let Sheldon back on the team if Penny is able to make Sheldon apologize, thinking it was impossible. Penny manages to do it by telling Sheldon to perform his apology with sarcasm. After a brief period back in the team, Sheldon is kicked off again and is seen in th last scene making an the algorithm for Penny's shoe app.