Indexing Category in php file Undefined inde

<?php 
$pageTitle = "Booking Schedule";
$selection = "booking"; 
include("inc/data.php");
include("inc/functions.php");
include("inc/header.php");
        ?>


        <div class="section catalog page">
      <div class="wrapper">
        <h1><?php echo $pageTitle; ?></h1>
       <?php include("inc/shop.php"); ?>        
        </div>
      </div>
<?php include("inc/footer.php"); ?>

<?php
$catalog = [];
$catalog[100] = [ "title" => "60 Minute Massage",
                 "img" => "http://i1.wp.com/www.tranquilinc.com/wp-content/uploads/2015/08/ID-10038310.jpg?resize=150%2C150",
                 "duration" => "1 Hour",
                 "value" => "$100",
                 "cost" => "$50",
                 "description" => "Get a hour massage from Tranquil Embodiment Massage in San Diego, CA. Comes complete with hot towels, aromatherapy, and your time doesnt start until your massage does.",
                 "time" => 60];
$catalog[150] = [ "title" => "90 Minute Massage",
                 "img" => "img/90m.png",
                 "duration" => "1 Hour and a Half",
                 "value" => "$150",
                 "cost" => "$75",
                 "description" => "Get a ninety minute massage from Tranquil Embodiment Massage in San Diego, CA. Comes complete with hot towels, aromatherapy, and your time doesnt start until your massage does.",
                 "time" => 90];
$catalog[200] = [ "title" => "2 Hour Massage",
                 "img" => "img/120m.png",
                 "duration" => "1 Hour",
                 "value" => "$100",
                 "cost" => "$50",
                 "description" => "Get a two hour massage from Tranquil Embodiment Massage in San Diego, CA. Comes complete with hot towels, aromatherapy, and your time doesnt start until your massage does.",
                 "time" => 120, ];
if (isset($_GET["cat"])) {
if ($_GET["cat"] == "60") { $pageTitle = "60 Minute Massage"; $selection = "60"; } Else if ($_GET["cat"] == "90") { $pageTitle = "90 Minute Massage"; $selection = "90";  } Else if ($_GET["cat"] == "120") { $pageTitle = "Two Hour Massage"; $selection = "120";  }  }
?>

<?php 
function get_item_html($id,$item) {
 $output =  "<li><a href='#'><img src='"
          . $item["img"]
          . "' alt='"
          . $item["title"] . " ' />"
          . "<br /><div class='crossOut'>" . $item["value"]
          . "</div><div class='hotSale'>" . $item["cost"] . "</div>"
          . "<p>View Details</p>"
          . "</a></li>"; 
return $output;

}

function array_category($catalog,$time) {
 $output = array();
  foreach ($catalog as $id => $item) {
                   if ($time == null OR strtolower($time) == strtolower($item["time"])) {
                     $sort = $item["title"];
                     $sort = ltrim($sort, "A ");                     
                     $sort = ltrim($sort, "The ");                     
                     $sort = ltrim($sort, "And ");
                   $output[$id] = $sort;
                   }  } 
  asort($output);
return array_keys ($output);} 


?>

<h1><?php if ($selection != null) {
  echo "<a href='booking.php'>Full Catalog</a> &gt; "; }
  echo $pageTitle;
  ?></h1>


<ul class="">
                <li class="Sixty Minute Massage<?php if ($selection == "60") { echo " on"; } ?>"><a href="booking.php?cat=60">Home</a></li>
                <li class="Ninety Minute Massage<?php if ($selection == "90") { echo " on"; } ?>"><a href="booking.php?cat=90">First Time</a></li>
                <li class="Two Hour Minute Massage<?php if ($selection == "120") { echo " on"; } ?>"><a href="booking.php?cat=120">Massage Therapists</a></li>
            </ul>
<ul class="items"><?php $times = array_category($catalog, $selection);
foreach ($time as $id) {
          echo get_item_html($id,$catalog[$id]);
} ?></ul>