Mixed Coin

Alice and Bob each have a coin. Alice's coin has probability $0 < p < 1/2$ of showing heads, while Bob's coin has probability $2p$ of showing heads. Let $A$ and $B$ be the indicator random variables of Alice and Bob having their respective coins show heads when flipped once. Find the value of $\lambda$ that minimizes the variance of $T_{\lambda} = \lambda A + \dfrac{1-\lambda}{2}B$ when $p = 1/3$.