I stumble upon a problem which i would like to pose it as "Optimization Problem". Given the dimension of larger and smaller rectangle, i would like to find the maximum number of smaller rectangle placed inside the larger rectangle such that the smaller rectangle doesnt overlap.
For example, if the dimension of larger rectangle is 4 x 5 and the dimension of smaller rectangle is 2 x 2, the maximum number of smaller rectangle which can be placed inside the larger rectangle is 4.
I came up with the following formulation which im not convinced ( A - area of larger rectangle, a - area of smaller rectangle and n- number of smaller rectangle)
$\max count \\ s.t\ A*count >= n*a*count \\$
Can anyone give me better formulation and lights to show