Simply, ～とする is adjectival (modifies a noun as a relative clause), and ～として is adverbial (modifies a verb as a te-form).
The next noun after the modifier in question is 日々. It's a noun that also works as an adverb, just like 明日, 去年, 今月, etc. If you say 利益を上げることを目的とする, it looks like it modifies 日々, and the whole sentence would look like "Companies conduct economic activities in the profit-pursuing days", which makes little sense because there is no such a thing as "non-profit-pursuing days" of a company. Instead, this modifier must modify the next verb, (経済活動を)行う.
Companies conduct economic activities every day with the purpose of making a profit.
In the English translation, you can see "with the purpose of making a profit" is modifying not "every day" but "conduct economic activities".
AをBに is also adverbial. It's perfectly fine to say 企業は利益を上げることを目的に日々経済活動を行っている, too.
By the way, What if there is no 日々?
Both are grammatical, but still, the former is more natural. In Sentence 1, 経済活動を行っている is adverbially modified by 利益を上げることを目的として ("Why companies do economic activities? Because they want to make a profit!"). This makes sense. In Sentence 2, 経済活動 is adjectivally modified by 利益を上げることを目的とする ("What kind of economic activity? The one that can make a profit!"). This sounds odd because it sounds as if there were such a thing as "non-profit-pursuing economic activity".