How many outlets can 1/2" copper pipe support?
According to Uniform Plumbing Code Table 6-5 (610.3), the Water Supply Fixture Units (wsfu) per fixture in a private residence are as follows:


Dishwasher = 1.5
Kitchen sink = 1.5
Washup sink = 0


So you're supplying 3 wsfu.

According to Table 6-6 (610.4), at 30-45 psi you can supply 3 wsfu with ½" pipe with a developed length of up to 100'.  46-60 psi you can have a developed length of up to 200', and greater that 60 psi can go up to 300'.

At 40' or less with 30 psi, ½" pipe can supply 6 wsfu.  So with a short run, you should have no problem using ½" pipe.