Equal priors, a costly miss

A classifier reads $X$. Under "negative" ($H_0$), $X \sim \text{Normal}(0, 1)$; under "positive" ($H_1$), $X \sim \text{Normal}(3, 1)$. The two states are equally likely, $\pi_0 = \pi_1 = 0.5$. A false alarm costs $1$ unit; a miss costs $9$ units. You declare "positive" when $X > c$.

Find the cost-minimizing cutoff $c$.