Step 1: Identify the property a shopping bag needs.
A carry bag must be thin, soft, flexible and tough, able to stretch without tearing.
Step 2: Compare the two polyethenes.
LDPE has many branches that stop chains from packing tightly, giving low density and high flexibility. HDPE has linear chains that pack tightly, giving stiffness and strength.
Step 3: Match flexibility to LDPE.
The branched, flexible LDPE is exactly what thin stretchable films and bags need, so it is the natural choice.
Step 4: Reject HDPE.
HDPE is rigid and strong, used for pipes, buckets and rigid containers, not soft bags.
Step 5: Reject polypropylene and PVC.
Polypropylene is used for ropes and moulded items, and PVC for pipes and insulation, neither for soft shopping bags.
Step 6: Conclude.
The flexible film for shopping bags is LDPE, option (B).
\[ \boxed{\text{LDPE (option B)}} \]