Additional Search Fields

I’m creating a product search functionality for a website I’m working on. The generated HTML code look something like the following:

<form action="<?=bloginfo('siteurl')?>" id="searchform" method="get">

   <input type="text" name="s" placeholder="Search for..." />

   <select style="background:#fff; width:180px; border:none; padding:10px;" name="s">
      <option name="cookers">Cookers</option>
      <option name="refrigerators">Refrigerators</option>
      <option name="clerical">Clerical</option>
      <option name="drinks-facilities">Drinks Facilities</option>
   </select>

   <input type="submit" value="Search" id="searchsubmit" />

</form>

The URL at present is ‘http://siteurl.com/search/searchterm’ and I’m unable to pass the selected category to the url to then display only products within the selected category.

Any suggestions? Or anyone know of any plugins worth a look?

Disclaimer: Don’t judge me on the inline styling 😉 that will go on the live site.