A businessman buys 1,440 dozen pens at $2.50 a dozen and then sells them at a price of 25¢ apiece. what is his total profit on the lot of pens?

Profit (P) is calculated by subtracting the total cost (C) from the total revenue (R). The calculations are shown below,

R = (1440 dozens) x (12 pieces / 1 dozen) x (25 cents / piece) = $4320

C = (1440 dozens) x ($2.50 / dozen) = $3600

Profit = R - C = $4320 - $3600 = $720

Thus, the businessman's profit is $720.