Although still a sophomore at college, John O'Hagan's son Billy-Sean has already created several commercial video games and is currently working on his most ambitious project to date: a game called K that purports to be a "simulation of the world." John O'Hagan has decided to set aside some office space for Billy-Sean against the northern wall in the headquarters penthouse. The construction of the partition will cost $8 per foot for the south wall and $12 per foot for the east and west walls. What are the dimensions of the office space with the largest area that can be provided for Billy-Sean with a budget of $432?

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