Step 1: Identify the time clause.
The phrase “By the time you reach New Jersey” refers to a specific moment in the future.
Step 2: Decide the appropriate tense.
To describe an action that will be in progress at a particular future time,
we use the future continuous tense:
\[
\text{will be + verb-ing}
\]
Step 3: Analyse the options.
Will shop — simple future; does not show the action in progress.
Will be shopping — correct; shows ongoing action at that future time.
Will be shipping — incorrect meaning in this context.
Both (B) and (C) — incorrect since (C) is not suitable.
Hence, the correct answer is
\[
\boxed{\text{Will be shopping}}
\]