Extra Efficient Elves

Santa has assigned Allie, Buzzy, and Chelly Elf the task of wrapping 240,000 presents. Santa wants the elves to use four types of wrapping paper: blue, red, green, and patterned, and to wrap a quarter of the presents in each type of paper.

Allie Elf can wrap presents at the rate of 3 presents per minute if she has blue wrapping paper, but only at the rate of 2 presents per minute if she has red wrapping paper. She drops down to only 1 present per minute if the paper is green or patterned.

Buzzy Elf can wrap presents at the rate of 2 presents per minute if the paper is blue or patterned. Otherwise, he wraps at 1 present per minute.

Chelly Elf can wrap presents at the rate of 1.5 presents per minute regardless of the type of paper.

The elves want to finish the job as fast they can. Who should use which paper in order to speed things up? And what is the minimum time required (to the nearest hour) if the elves are to work non-stop?

See the solutions