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 oresentine Micromedia is currently planning a two$-$day seminar on the use of Microsoft Excel in statistical analysis. The projected fee for the seminar is $$615$ per student. The cost for the conf instructor compensation, lab assistants, and promotion is $$10,585.$ Micromedia rents computers for its seminars at a cost of $$125$ 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.

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

$P=$

$($c$)$ Micromedia has forecast an enrollment of $55$ students for the seminar. How much profit will be earned if their forecast is accurate?

$P(55)=$$

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

$x=17\mathrm{.}2113821$