I'm asked to pack the maximum number of 10m^2 circle into a 257 x 157m rectangle. After a lot of research, I found out that there are no optimal solution. So, i try to pack as many as possible (taking this website as reference):
1) First, I tried to place them in rectangular pattern:
- I had the width 257/d (diameter) -> I got about 72.024 --> So along the width, i can place 72 circle.
- I had the height 157/d (diameter) -> I got about 43.999 --> So along the height, i can place 43 circle.
--> That means in this case, i can fit in 43*72= 3096 circles
2) Then I try triangular pattern, which can fit more circles, 3575 circles. However, I find my math calculation kinda inefficient, long, and not correct in any other cases.
So my question is: Did I calculate it in a correct way? Are there any other more effective calculation methods?
Because in later question, it asks me to find the area of the circle to so that we get the maximum profit. Giving the profit of each circle is: P(a) = 200 - 200/a (a is the area of the circle)