Problem obtaining MAX values FROM TABLE

I am having a problem with a query, I have a view which produces something
like this:

b_id company_name product_count product_type
------------------------------------------------
29 "company 1" 1 "a"
29 "company 2" 1 "b"
29 "company 3" 3 "a"
27 "company 4" 1 "c"
27 "company 4" 4 "d"
24 "company 5" 3 "a"
24 "company 5" 5 "c"
24 "company 5" 2 "d"
-------------------------------------------------

I need to write a query which returns each company together with the
highest product_count and its associated product type so the result should
look like this:

b_id company_name product_count product_type
------------------------------------------------
29 "company 1" 1 "a"
29 "company 2" 1 "b"
29 "company 3" 3 "a"
27 "company 4" 4 "d"
24 "company 5" 5 "c"
-------------------------------------------------

I have tried the following query:

SELECT company, MAX(type_count), product_type FROM buyer_product_frequencies

GROUP BY company, product_type

But in this case it just produces the same results as are in the first
table. If I drop product_type from the query I get the right result but I
don't have the product type which I need. This problem is driving me mad! so
any assistance would be greatly appreciated.

Many thanks,

Mike Farewell