Hello! I am given the following question on output allocation and total cost for my microeconomics graduate course. I am having getting started on the 1st two problems! In help you could provide would be so beneficial. Thank you!

A firm has two plants that it may use to produce its output.

The first plant's cost function is C1(Q1) = (Q1)^2 and the second plant's cost function is C2(Q2) = Q2 + 21*(Q2)^2

1. Suppose the firm has target total out Q = Q1 +Q2 > 0. How should the firm divide total output Q between the two plants in order to minimize costs?
2. What is the resulting total cost for the firm C(Q), if output is allocated in the cost minimizing way?