II$.$ Zed design model $(30$pts$)$: Given an online DVD rental system $($e$.$g$.$ Blockbuster$),$ define the search operation and checkout operation using correct $Z$ notation. Please following the steps below:

Define the necessary data and operations $(4$pts$).$

Define the initial schemas of all the data in step $(1)$ for the DVD rental system. $(12$pts$)$

Define the operation schemas for the search and purchase operations, you need to specify operation successful or failure, respectively. $(14$pts$)$