Micromedia offers computer training seminars on a variety of topics. In the seminars each student works at a personal computer, practicing the particular activity that the instructor is presenting. Micromedia is currently planning a two$-$day seminar on the use of Microsoft Excel in statistical analysis. The projected fee for the seminar is $$565$ pe student. The cost for the conference room, instructor compensation, lab assistants, and promotion is $$7,370.$ Micromedia rents computers for its seminars at a cost of $$115$ per computer per day.

$($a$)$ Develop a model for the total cost $(C)$ to put on the seminar. Let $x$ represent the number of students who enroll in the seminar.

$C=$

$($b$)$ Develop a model for the total profit $(P)$ if $x$ students enroll in the seminar.

$P=$

$($c$)$ Micromedia has forecast an enrollment of $50$ students for the seminar. How much profit will be earned if their forecast is accurate?

$P(50)=$$

$($d$)$ Compute the break$-$even point.

$x=$