Can somebody please help me do part A? No idea where to start

A)
lim as x -> infinity: 50x/ln(x+2) + 15000 = infinity/infinity

this is an indeterminate form so we use l'Hosipital's Rule. Which means we take the derivative of the numerator and the denominator separately and re-apply the limit.
(50x)'
-----------
(ln(x+2))'

So we have:
50
------------- = 50x + 100
1
-------
x+2

which = lim x -> infinity: 50x = infinity (the plus 100 and 15000 can be removed from the equation as infinity + anything is still infinity)

Now as for this being reasonable from an economics perspective. I have no idea what it's asking. It seems logical that creating an infinity amount of widgets will have an infinite cost yes. but it seems unreasonable to consider creating an infinite amount of widgets.

Reasonable - No
Creating an infinite amount of anything from an economics perspective would be a financial loss, there are not enough people to buy infinite. You must create a supply within demand.