WMI to reboot remote machine

I found this code on an old thread to shutdown the local machine:

using System.Management;

void Shutdown()
{
    ManagementBaseObject mboShutdown = null;
    ManagementClass mcWin32 = new ManagementClass("Win32_OperatingSystem");
    mcWin32.Get();

    // You can't shutdown without security privileges
    mcWin32.Scope.Options.EnablePrivileges = true;
    ManagementBaseObject mboShutdownParams =
             mcWin32.GetMethodParameters("Win32Shutdown");

    // Flag 1 means we want to shut down the system. Use "2" to reboot.
    mboShutdownParams["Flags"] = "1";
    mboShutdownParams["Reserved"] = "0";
    foreach (ManagementObject manObj in mcWin32.GetInstances())
    {
        mboShutdown = manObj.InvokeMethod("Win32Shutdown", 
                                       mboShutdownParams, null);
    }
}

Is it possible to use a similar WMI method to reboot flag "2" a remote machine, for which i only have machine name, not IPaddress.

EDIT: I currently have:

SearchResultCollection allMachinesCollected = machineSearch.FindAll();
Methods myMethods = new Methods();
string pcName;
ArrayList allComputers = new ArrayList();
foreach (SearchResult oneMachine in allMachinesCollected)
{
    //pcName = oneMachine.Properties.PropertyNames.ToString();
    pcName = oneMachine.Properties["name"][0].ToString();
    allComputers.Add(pcName);
    MessageBox.Show(pcName + "has been sent the restart command.");
    Process.Start("shutdown.exe", "-r -f -t 0 -m \\" + pcName);
}

but this doesn't work, and I would prefer WMI going forward.