I think, firm 2 after the acquisition of firm 1, it will have two different production plants. In order to find optimal quantity and price, because it has become monopoly, we should find marginal cost of these two plants and equate it with the marginal revenue.
Firm 1' marginal cost:
$f(K,L)=min(K,L) $
$K=L=Q$
$TC=w\times Q+r\times Q=Q\times(w+r)$
$MC1=w+r$
Firm 2' marginal cost:
$Q=f(K,L)=L^{0.5}\times K^{0.5} \rightarrow L=Q^{2}/K \rightarrow K=Q^{2}/L $
$TC=w\times Q^{2}/K+r\times Q^{2}/L$
$MC2=(2\times Q \times w)/K+ (2\times Q \times r)/L$
Then this firm should use it's production plant which was using before acquisition until the $MC1=MC2$ and then remaining production should be held by production plant that was bought from Firm 1 until first $MC2=MR=(Q\times P) (dTR/dQ)$ and $MC1=MR$ .
