DSE 2011 Question 48: Costs of production

A firm has an order to supply 20 units of output. It can divide production across two plants, 1 and 2, with cost functions $c_{1}(q_{1})=q_{1}^{2}$ and $c_{2}(q_{2})=3q_{2}^{2}$, subject to $q_{1}+q_{2}=20$. To meet the total production target at minimum cost, the amount of output the firm should produce in its first plant is