Add a docker build step.

backend/Dockerfile

@@ -0,0 +1,47 @@
+# Multi-stage Dockerfile for Rust backend
+FROM rust:1.90-alpine as builder
+
+# Install build dependencies
+RUN apk add --no-cache \
+    musl-dev \
+    pkgconfig \
+    openssl-dev \
+    clang
+
+# Set working directory
+WORKDIR /app
+
+# Copy Cargo files for dependency caching
+COPY Cargo.toml Cargo.lock ./
+
+# Create a dummy main.rs to build dependencies
+RUN mkdir src && echo "fn main() {}" > src/main.rs
+
+# Build dependencies (cached layer)
+RUN cargo build --release && rm -rf src/
+
+# Copy source code
+COPY src/ src/
+COPY migrations/ migrations/
+
+# Build the application
+RUN cargo build --release
+
+# Runtime stage
+FROM alpine:latest
+
+# Install runtime dependencies
+RUN apk add --no-cache ca-certificates curl
+
+# Copy the binary from builder stage
+COPY --from=builder /app/target/release/backend /usr/local/bin/app
+
+# Expose port
+EXPOSE 3000
+
+# Health check
+HEALTHCHECK --interval=30s --timeout=3s --start-period=5s --retries=3 \
+    CMD curl -f http://localhost:3000/health || exit 1
+
+# Run the application
+CMD ["app"]