38. Cryptography 5

Solve Cryptography 4 first.

Suppose that observing each letter takes time and can be translated into a cost $c_L$ per letter and misclassifying the language can be translated into a cost of $c_\epsilon$. Find the number of letter $n$ upon which your total cost $C_n(n, \Upsilon, \Phi, k, c_L, c_\epsilon)$ is minimised as a function of $n, \Upsilon, \Phi, k, c_L$ and $c_\epsilon$.