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The phrase "at a maximum capacity" is correct and usable in written English
It can be used when referring to the highest level of occupancy or utilization of a space, system, or resource. Example: "The concert hall was filled to at a maximum capacity, leaving no empty seats."
Exact(3)
DFC300 produces electricity at a maximum capacity of 280 kW.
Generators G-19, G-20 and G-21 in the Third Powerplant have a 600 MW installed capacity but can operate at a maximum capacity of 690 MW which brings the overall maximum capacity of the dam's power facilities to 7,079 MW.
You'll be pushed to perform at a maximum capacity.
Similar(57)
Methane sorption at 25 °C demonstrated a maximum capacity above 46 cm3/g (45 vol/vol or 3.1 wt.%) at atmospheric pressure.
Space is an issue at the wedding, as there is a maximum capacity of 200 at the reception venue.
At 115,000 tons, she carries a maximum capacity of 4,000 passengers and 1000 officers and crew.
At the time, the facility had a maximum capacity of 200 prisoners.
The same trend was observed for P2; at a maximum loading capacity of 49 wt % the largest Rh value was observed with Rh,mic(P2+PTX) = 23.8 ± 0.3 nm.
He added: "The inquiry will forensically examine what went wrong at Heathrow, and look fundamentally at our ability to prepare and respond more effectively to periods of bad weather at an airport operating at its maximum capacity.
To further investigate how organisms with forward polymerases fared in competition with organisms with reverse polymerases, specifically to see if an equilibrium was possible between the two varieties, we performed a number of simulations starting with an environment already at its maximum capacity.
The response of a colony to starvation is classically described as an all-or-nothing response: the stocks present in the colony must be below a critical value for mass recruitement to occur and the colony harvests at maximum capacity until a threshold volume is reached.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com