Step 1: Calculate the number of moles of A and B.
The number of moles of A:
\[
\frac{36}{60} = 0.6 \, \text{mol}.
\]
The number of moles of B:
\[
\frac{54}{80} = 0.675 \, \text{mol}.
\]
Step 2: Use stoichiometry.
The reaction between A and B is:
\[
A + B \rightarrow AB_2.
\]
From the stoichiometry, 1 mole of A reacts with 1 mole of B to form 1 mole of AB\(_2\). Therefore, A is the limiting reagent because there are fewer moles of A than B.
Step 3: Conclusion.
Since A is the limiting reagent, it will determine the amount of AB\(_2\) formed.
Final Answer:
\[
\boxed{\text{Limiting Reagent is B}}.
\]