Matt accepts a job offer as a Chemical Engineer in the Research and Development department of Tulip Inc., a paint manufacturing company. After accepting the job offer, he signs an employment contract stating that the results of his research would be the sole property of the company. Matt comes up with an innovative paint formula that can withstand extreme temperatures. He receives a promotion and a handsome package for his work. However, he is annoyed that the formula was not patented in his name. In the context of the given scenario, which of the following statements is true?

a$.$

Since the formula can be patented only by Matt, the company is legally required to pay him $30$ percent of the total profits gained.

b$.$

A heavy fine can be imposed on the company for drawing a contract that is unenforceable.

c$.$

Matt's formula is his own intellectual property, and he has the right to use it as he sees fit.

d$.$

The innovation made by Matt on the job falls under the management and control of the organization