OK lets try that again:

How could i compare these two arrays in order to create a new array:

Array One
--------------
Posted_Apps Array
(
[0] => Array
(
[lender_id] => 1
[app_count] => 2
)

[1] => Array
(
[lender_id] => 3
[app_count] => 4
)

)
--------------
Array 2
-----------------
Eligible_LendersArray
(
[0] => Array
(
[lender_id] => 3
[daily_max] => 100
)

[1] => Array
(
[lender_id] => 5
[daily_max] => 100
)

[2] => Array
(
[lender_id] => 4
[daily_max] => 100
)

)

I want the comparison to be such that each instance of lender_id in
array one is compared to the matching instance in the second array
regarding the daily_max value and create a new array of eligible
lender_ids for those that are equal or LESS than the daily max of
array two.

i.e. 

New_array
-------------
(
[0] => 3
[1] => 5
[2] => 4
)

The new array should show all lenders who have daily_max LESS THAN or
EQUAL TO app_count.

Z

This works to see if daily_max is less than or equal to app_count:

$new_arrray = NULL;

foreach ($Posted_Apps as $PA) {
  foreach ($Eligible_Lenders as $EL) {
    if($PA['lender_id'] == $EL['lender_id']
       && $EL['lender_id'] <= $PA['app_count']) {
         
         $new_array[] = $EL['lender_id'];
    }
  }
}

----------

This works to see if app_count is less than or equal to daily_max:

$new_arrray = NULL;

foreach ($Posted_Apps as $PA) {
  foreach ($Eligible_Lenders as $EL) {
    if($PA['lender_id'] == $EL['lender_id']
       && $EL['lender_id'] > $PA['app_count']) {
         
         $new_array[] = $EL['lender_id'];
    }
  }
}

$new_array will contain the IDs of lenders who meet the requirement.

DISREGARD THE FIRST COMMENT. I just noticed a bug. Here's the correct
code. $new_array will contain the IDs of eligible lenders.

--------------------------------------------------

Works if daily_max is less than or equal to app_count:

$new_arrray = NULL;

foreach ($Posted_Apps as $PA) {
  foreach ($Eligible_Lenders as $EL) {
    if($PA['lender_id'] == $EL['lender_id']
       && $EL['daily_max'] <= $PA['app_count']) {
         
         $new_array[] = $EL['lender_id'];
    }
  }
}

--------------------------------------------------

Works if app_count is less than or equal to daily_max:

$new_arrray = NULL;

foreach ($Posted_Apps as $PA) {
  foreach ($Eligible_Lenders as $EL) {
    if($PA['lender_id'] == $EL['lender_id']
       && $EL['daily_max'] > $PA['app_count']) {
         
         $new_array[] = $EL['lender_id'];
    }
  }
}