$4.$ Many customers are interested in purchasing limited$-$edition sneakers from an online retail store, but these items often sell out quickly. The store wants to implement a feature where customers can sign up to receive notifications when these sneakers are back in stock.

Tasks:

$($a$)$ Sequence Diagram:

Create a sequence diagram that illustrates the interactions between the system's components when a new batch of limited$-$edition sneakers becomes available, and notifications are sent out to subscribed customers.

$($b$)$ Class Diagram:

Develop a class diagram that represents the structure of this scenario. Indicate the relationships between classes, such as associations, inheritances, and dependencies. Don$$t forget multiplicity.

$($c$)$ Please ensure that your diagrams are clear, well$-$organized, and accurately reflect the requirements. Include appropriate methods and attributes for each class and interaction in your diagrams.

$($d$)$ Imagine that you are developing a lighting system. A switch has $$on$$ and $$off$$ states. When the switch is turned to $$on$,$ the light should be turned on$.$ Otherwise, the light should be turned off. Suppose that we have different types of switches, such as a regular switch attaching to the wall or a remote control switch that can remotely turn on$/$off the light. Please draw a statechart diagram and a class diagram for your analysis and design.

$($e$)$ Imagine that you will develop a web system for a rural area, which only has very slow Internet connection. As downloading images is pretty time consuming, you want to make a place holder for the image when initializing a web page. We want to show the text portion as soon as possible. The real images are displayed after the text portion has been downloaded. This strategy is good because users have something to see when they try to open a web page. Otherwise, they will lose patience if they have to wait for a long time to see the web page. Please use the class diagram to make the design.