Advice on Solving a Problem of Oval Proportions

[FoxLivings]

Hi All,


I'm working on a problem and wondering if anyone has a potential solution, explanation or approach!

I'm helping to plan an event and trying to figure out a spacial issue:

The event (a fair) will be held in an oval tent with dimensions 57'X76'. Each Participant in the event will have a designated booth size of 7'X9'. There are 30 participant booths that need to fit into the oval tent.

What's the best way to arrange the booths to fit in the tent? Is it possible? Could you explain how you worked out your solution?

Other considerations:

-The tent needs two entrance/exit ways (two doors total)
-Ailes between booths must be at least 5 feet wide
-The tent has two structural poles that are placed towards the center of the tent, about 30 feet in from the most lengthwise ends.
-Booths must be presented in a way that looks nice and allows orderly flow of participants and visitors.
-Many participants may not have a "backside" to their booth. The front typically looks nicest.

Thank you for your ideas and thoughts!

Lark`

 

[Deleted member 4993]

Hi All,


I'm working on a problem and wondering if anyone has a potential solution, explanation or approach!

I'm helping to plan an event and trying to figure out a spacial issue:

The event (a fair) will be held in an oval tent with dimensions 57'X76'. Each Participant in the event will have a designated booth size of 7'X9'. There are 30 participant booths that need to fit into the oval tent.

What's the best way to arrange the booths to fit in the tent? Is it possible? Could you explain how you worked out your solution?

Other considerations:

-The tent needs two entrance/exit ways (two doors total)
-Ailes between booths must be at least 5 feet wide
-The tent has two structural poles that are placed towards the center of the tent, about 30 feet in from the most lengthwise ends.
-Booths must be presented in a way that looks nice and allows orderly flow of participants and visitors.
-Many participants may not have a "backside" to their booth. The front typically looks nicest.

Thank you for your ideas and thoughts!

Lark`

Please share your work/thoughts about this assignment.

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[Dr.Peterson]

I'd make a scale drawing of the tent and 30 booths, and try various ways of laying it out. Much of the work will not be mathematical but practical and aesthetic.

I did check mathematically that the area of the tent is about 54 times the area of one booth, so at least it is not impossible to fit 30 booths! You could adjust this to determine how many aisles in either direction can fit, which could eliminate some possible configurations.

 

[LCKurtz]

I had a bit of time to kill, so I made an approximate sketch. It's going to be close. If you need all booths to be separated by aisles as I have sketched in the first picture below, you can't do it. In the second picture I have removed all the vertical aisles, and you can squeeze in 32. You need to do something about vertical aisles. Here are my two rough sketches: