Dynamically set select-options with JavaScript

wellyou have almost done it all:

var optionsAsString = "";
for(var i = 0; i < productArray.length; i++) {
    optionsAsString += "<option value="" + productArray[i] + "">" + productArray[i] + "</option>";
}
$( 'select[name="inptProduct"]' ).append( optionsAsString );

EDIT removed $ wrapper around last optionsAsString as append automatically converts strings