A record company makes an initial investment of $$5,000$ to prepare the songs for a musical album. The cost of manufacturing and recording each disc is $$4.$ Additionally, the record company must pay the singer $$1$ per record for royalties.

It is decided that the sales price of the album will be $$15$

It is requested:

a$.$ The profit function $($profits minus expenses$)$ of the company based on the number of records sold. Represent your graph.

b$.$ The number of records that must be sold for the company to make a profit of $$100,000.$

c$.$ What are the benefits if only $200$ records are sold?