Cost-optimal cutoff with a wider spread

A sensor reads $X$. Under "normal" ($H_0$), $X \sim \text{Normal}(10, 2)$ with prior $\pi_0 = 0.95$. Under "fault" ($H_1$), $X \sim \text{Normal}(18, 2)$ with prior $\pi_1 = 0.05$. A false alarm costs $2$ units; a missed fault costs $50$ units. You declare "fault" when $X > c$.

Find the cost-minimizing cutoff $c$.