We can apply dynamic programming to this problem. Note that for each state it suffices to track the month and the number of cue balls. Since Veshy can have at most ~100~ cue balls, this is only ~100N~ states, which is fine.

For each state, we consider selling some or all of his cue balls. Let ~dp[m][i]~ be the maximum money we can have after ~m~ months when we own ~i~ cue balls. Then:

$$\displaystyle dp[m][i] = \max_{0 \le j \le \min(100-i, Y_i)} dp[m-1][i+j] + j \times s_i$$

Also, after we consider selling cue balls, we can consider buying some cue balls.

$$\displaystyle dp[m][i] = \max_{0 \le j \le \min(i, X_i)} dp[m-1][i-j] - j \times b_i$$

Finally, make sure to subtract the maintenance costs from each state. (So ~dp[m][i] := dp[m][i] - M \times i~ for ~1 \le i \le 100~)

Time Complexity: ~\mathcal O(NK^2)~, where ~K~ is the number of cue balls we can hold at once. In this case, it is ~100~.