The cost-minimizing decision threshold

A monitoring system reads a value $X$. Under background ($H_0$), $X \sim \text{Normal}(0, 1)$ with prior probability $\pi_0 = 0.9$. Under an anomaly ($H_1$), $X \sim \text{Normal}(4, 1)$ with prior probability $\pi_1 = 0.1$. A false alarm (declaring an anomaly when there is none) costs $1$ unit; a missed anomaly costs $27$ units. You will declare "anomaly" whenever $X > c$.

Find the cutoff $c$ that minimizes the expected cost.