beauftragen
to commission
To give a person or company an official assignment or task.
Wir haben einen Architekten damit beauftragt, das neue Haus zu planen.
We commissioned an architect to plan the new house.

to commission
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to commission
To give a person or company an official assignment or task.
Wir haben einen Architekten damit beauftragt, das neue Haus zu planen.
We commissioned an architect to plan the new house.

'Beauftragen' (to commission) is an inseparable verb. The prefix 'be-' remains firmly attached to the verb stem 'auftragen' in all tenses and sentence constructions.
Sie beauftragte einen Maler mit der Renovierung ihrer Wohnung.
She commissioned a painter to renovate her apartment.
The verb 'beauftragen' (to commission) is derived from the noun 'der Auftrag' (the assignment/order). To commission someone means to give that person an assignment.
Der Auftrag lautet, die Webseite bis Ende des Monats fertigzustellen.
The assignment is to finish the website by the end of the month.
There are two typical sentence constructions: You can commission someone (accusative) 'mit etwas' (with something, dative), or commission someone (accusative) to 'etwas zu tun' (to do something, infinitive with zu).
Ich habe eine Firma mit der Reinigung beauftragt.
I commissioned a company to do the cleaning.
The accusative object is typically a person or company that provides a service, for example commissioning 'einen Anwalt' (a lawyer), 'einen Handwerker' (a tradesperson), or 'eine Agentur' (an agency).
Für die Reparatur müssen wir einen Spezialisten beauftragen.
We need to commission a specialist for the repair.
to let / to have
'lassen' and 'beauftragen' can both mean that you do not do something yourself, but want another person to do it. 'lassen' is more general and very common in everyday language: you 'das Auto reparieren lassen' (have the car repaired) or 'die Haare schneiden lassen' (have your hair cut). 'beauftragen' sounds more official and more specific. You give a person or company an assignment, often for money or with a clearly defined task. Learners may confuse the words because in both cases someone else takes action. If it is only about someone doing something for you, 'lassen' often fits. If an official assignment is meant, 'beauftragen' fits better.

Die Firma beauftragt einen Handwerker mit der Reparatur.
The company commissions a tradesperson to do the repair.
Wir lassen die Heizung morgen reparieren.
We are having the heating repaired tomorrow.