Question #$1$: $[20$ points$]$

The Toyota dealerships in the Dallas area have decided to design a database that keeps a record of all cars at all dealerships.

Each dealership has a name, dealership #$,$ location and space $($lot in square feet$).$

Cars are divided into new and used. Each car has a year, make, and model.

Cars may contain options that go by option #$,$ descriptions, and list price.

Options are divided into manufacturer and dealer$-$installed options.

For new cars, there is a manufacturer's invoice with a date, invoice$\_$amount and a dealer$\_$discount$\_$amount.

Used cars have a bill of sale with seller's name, seller address, date and amount.

When a car is sold by a salesman, a record of the sale transaction is kept with a date, amount, and remarks describing other details.

Information about salesmen includes their names, phone #$,$ SS#$,$ and monthly sales quota.

Make any missing assumptions you need to make $-$ state them clearly and proceed.

Draw an enhanced entity$-$relationship diagram for this database. You may add extra attributes $($beyond those specified above$)$ as needed. Be sure to indicate the mapping cardinalities and the participation constraints. Also, designate a reasonable primary key for each entity set in your diagram.