If I read the question correctly, your final answer is not correct.

The probabilities (P(0 defectives), P(1 defective), P(2 defectives)) you calculated are correct, but your follow-up steps seem hinky. It is said that it costs 100 pounds to inspect a sample. You will atleast inspect one sample a day. Hence the expected cost should be at least 100 pounds.

So the next question is: In which case do you sample more than once in a day?