I am confused about the Short Run Total Cost function of this problem.

If the firm's production function is $F(K,L) = K+ln(L)$ derive the short run total cost function.

I was able to solve the Short run total cost function, but my TA had 2 cases for her function whereas I only had 1 part of her function.

I got $TC= W*e^{q-K} + r\bar{K}$ for all $q$ but my TA had 2 cases for $q$. Specifically, when $q<\bar{K}$ and $q>\bar{K}$

Thank you.

I am confused about the Short Run Total Cost function of this problem.

If the firm's production function is $F(K,L) = K+\ln(L)$ derive the short run total cost function.

I was able to solve the Short run total cost function, but my TA had 2 cases for her function whereas I only had 1 part of her function.

I got $TC= W*e^{q-K} + r\bar{K}$ for all $q$ but my TA had 2 cases for $q$. Specifically, when $q<\bar{K}$ and $q>\bar{K}$

Thank you.