app|lib|app.ex

defmodule App do
  def start(_type, _args) do
    port = String.to_integer(System.get_env("PORT"))
    :cowboy.start_clear(:http, 
      [{:port, port}],
      %{env: %{ dispatch: build_dispatch_config() }}
      )
  end
  
  def build_dispatch_config do
    :cowboy_router.compile([
        { :_, [
            {"/", App.PageHandler, []},
          ]
        }
      ])
  end
end

app|lib|page_handler.ex

defmodule App.PageHandler do
  def init(req, state) do
    handle(req, state)
  end
  
  def handle(request, state) do
    req = :cowboy_req.reply(200, %{"content-type" => "application/json"}, "{}", request)
    
    {:ok, req, state}
  end

end

app|mix.exs

defmodule App.MixProject do
  use Mix.Project

  def project do
    [
      app: :app,
      version: "0.1.0",
      elixir: "~> 1.7",
      start_permanent: Mix.env() == :prod,
      deps: deps()
    ]
  end

  # Run "mix help compile.app" to learn about applications.
  def application do
    [
      extra_applications: [:logger],
      mod: { App, [] },
      applications: [:cowboy, :ranch],
    ]
  end

  # Run "mix help deps" to learn about dependencies.
  defp deps do
    [
      {:cowboy, "~> 2.6.0"},
      # {:dep_from_git, git: "https://github.com/elixir-lang/my_dep.git", tag: "0.1.0"},
    ]
  end
end

Dockerfile

FROM elixir:latest

# Set exposed ports
EXPOSE 80
ENV PORT=80

ENV MIX_ENV=prod

ADD app/ ./
ADD script.sh ./

RUN mix local.hex --force && \
    mix local.rebar --force && \
    mix deps.clean --all && \
    mix deps.get

CMD . ./script.sh

script.sh

#!/bin/bash

iex -S mix run