The phrase "at a profit" is correct usage in written English. You can use it to describe the amount of benefit derived from an activity. For example, "The company was able to sell the excess inventory at a profit.".
"They'll get paid back at a profit".
And it is running at a profit.
"Merchants can operate them at a profit".
When they do, the activists sell at a profit.
The tickets can be resold at a profit, too.
He wants to sell his stock at a profit.
"The city is getting paid back at a profit".
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Ha Thuy Vy
MA of Applied Linguistic, Maquarie University, Australia