Faturamos mais a fim de que o lucro fique alto.

Faturamos comes from faturar. In business Portuguese, faturar usually means to bill, to invoice, or more broadly to generate revenue / make sales.

So faturamos mais means something like:

• we bill more
• we make more revenue
• we sell more

It does not automatically mean we make more profit. That is important here, because the sentence separately mentions o lucro (the profit).

It can be either, depending on context.

For nós forms of many -ar verbs, the present indicative and the preterite look the same:

• nós faturamos = we bill / we make revenue
• nós faturamos = we billed / we made revenue

In this sentence, the most natural reading is usually present:

• We bill/make more so that the profit stays high.

The rest of the sentence, especially the idea of purpose in a fim de que, makes the present reading more likely.

A fim de que means so that, in order that, or for the purpose that.

It introduces a purpose:

• Faturamos mais = we make more revenue
• a fim de que o lucro fique alto = so that the profit stays high

It is a fairly formal expression. In everyday speech, Brazilians often use para que instead.

They are very close in meaning. Both can mean so that or in order that.

• a fim de que = more formal, more written, more polished
• para que = more common in everyday speech

So these are very similar:

• Faturamos mais a fim de que o lucro fique alto.
• Faturamos mais para que o lucro fique alto.

The first sounds more formal or businesslike.

Because a fim de que triggers the subjunctive.

In Portuguese, when you express:

• purpose
• intention
• desired result
• something not presented as a simple fact

you often use the subjunctive in the following clause.

So:

• ...que o lucro fique alto = ...so that the profit may stay/remain high

If you said fica, that would be the indicative, which does not fit this structure as well.

Fique is the present subjunctive of ficar for ele/ela/você.

Here the subject is o lucro, which is grammatically third person singular, so Portuguese uses the same verb form as ele/ela:

• que eu fique
• que você fique
• que ele/ela fique
• que nós fiquemos
• que vocês fiquem
• que eles/elas fiquem

So o lucro fique = the profit stay/remain.

Ficar alto here means to stay high, to remain high, or to end up high depending on context.

With things like prices, numbers, levels, and profit, Portuguese often uses ficar + adjective naturally:

• o preço fica alto = the price stays/is high
• o lucro fique alto = the profit stays/remains high

It is a very normal structure in Portuguese.

Because in Portuguese, descriptive adjectives usually come after the noun.

So:

• lucro alto = high profit

That is the normal order.

If you put the adjective before the noun, the meaning can become more literary, emphatic, or stylistically marked. In ordinary business language, lucro alto is the natural choice.

Mais modifies the verb faturamos.

So faturamos mais means:

• we bill more
• we generate more revenue
• we make more in sales

It is not directly modifying lucro. The idea is:

1. we increase revenue,
2. so that profit stays high.

This is a very common point of confusion.

• a fim de = for the purpose of, in order to
• afim = related, similar, compatible

So in your sentence, it must be a fim de que, written as three words.

Examples:

• Estudamos a fim de passar. = We study in order to pass.
• São áreas afins. = They are related fields.

Yes. A very natural rewrite is:

• Faturamos mais para que o lucro fique alto.

That means the same thing and sounds more everyday and conversational.

If you want to keep the same formal tone, a fim de que is perfectly good. If you want a more common spoken version, para que is usually the better choice.

Because Portuguese usually prefers para que + subjunctive when the second clause has its own subject.

Here:

• main clause subject: nós in faturamos
• subordinate clause subject: o lucro in fique

So the standard form is:

• para que o lucro fique alto
• a fim de que o lucro fique alto

Using an infinitive is more natural when the subject stays the same, for example:

• Faturamos mais para aumentar o lucro.

There, the understood subject of aumentar is still nós.