The chairman pointed out in favour of the manager that the profitability of the industrial plant had….. since he took over the administration.

The correct option is increased.

Let us analyze the context of the sentence to determine the most appropriate word to complete it.

The sentence reads: "The chairman pointed out in favour of the manager that the profitability of the industrial plant had….. since he took over the administration."

1. Key phrase analysis:
The phrase "in favour of" indicates that the chairman is presenting a positive aspect, support, or recommendation for the manager based on his performance.

2. Evaluating the options:
- arisen: Means to originate, result, or stand up. It is not typically used to describe changes in financial metrics like profitability.
- declined: Means decreased or deteriorated. This represents a negative outcome, which contradicts the phrase "in favour of".
- added: Means joined or united to increase size or quantity, but contextually "profitability had added" is grammatically incorrect.
- increased: Means became greater in size, amount, or degree. A rise in profitability is a positive result, which directly supports pointing out something "in favour of" the manager.

Therefore, the word increased fits both contextually and grammatically to show that the manager achieved a favorable outcome (higher profitability) during his administration.