A software engineer coded a program with two parts but the parts may contain errors (bugs). He has a total time budget T > 0 to debug (eliminate errors) of his codes. If he spends time t1 on Part 1 of the program and t2 on Part 2 of the program, the probability that the program works correctly is (11 exp(t1))(12 exp(t2)) where 1; 2 (0; 1) are known constants. The engineer chooses (t1; t2) to maximize the probability that the program works correctly. Find the optimal (t1; t2) for her.