To extract the mysql_installer.msi file from resources and install it using C#, you can use the following code:

using System;
using System.IO;
using System.Reflection;

namespace MySQLInstaller
{
    class Program
    {
        static void Main(string[] args)
        {
            string msiFileName = "mysql_installer.msi"; // Name of the MSI file in resources

            // Get the current assembly
            Assembly currentAssembly = Assembly.GetExecutingAssembly();

            // Get the resource stream of the MSI file
            using (Stream resourceStream = currentAssembly.GetManifestResourceStream("YourNamespace." + msiFileName))
            {
                if (resourceStream == null)
                {
                    Console.WriteLine("Failed to find the resource: " + msiFileName);
                    return;
                }

                // Create a temporary file path to save the MSI file
                string tempPath = Path.Combine(Path.GetTempPath(), msiFileName);

                // Save the MSI file from the resource stream to the temporary file path
                using (FileStream fileStream = File.Create(tempPath))
                {
                    resourceStream.CopyTo(fileStream);
                }

                // Run the MSI file using the Windows Installer
                System.Diagnostics.Process.Start("msiexec", "/i \"" + tempPath + "\"");
            }

            Console.WriteLine("Installation completed.");
            Console.ReadLine();
        }
    }
}

Make sure to replace "YourNamespace" with the appropriate namespace in your project. This code assumes that the mysql_installer.msi file is added as a resource to your project.

When you run this code, it will extract the mysql_installer.msi file from the resources, save it to a temporary location, and then execute the MSI file using the Windows Installer (msiexec). This will initiate the installation process of MySQL based on the provided MSI file.

Please note that you may need to adjust the code according to your specific requirements, such as handling any errors or specifying additional installation options.