The Industrial Engineering department is considering $6$ new classes with an estimated profit $($tuition $$ faculty pay$)$ in thousands of dollars and enrollment in number of students as follows:

Courses to Offer

$(1)$ System Optimization II

$(2)$ Business Architecture

$(3)$ Leadership & Diversity

$(4)$ Technical Leadership

$(5)$ Quality Engineering

$(6)$ Systems Engineering II

Profit $($thousands$)$

$14$

$12$

$18$

$18$

$10$

$11$

Estimated Enrollment

$36$

$32$

$42$

$45$

$22$

$28$

$$

The total enrollment available for these courses is $100.$

Courses $1$ and $2$ cannot be taken at the same time

Courses $3$ and $4$ cannot be taken at the same time

There are no such restrictions for courses $5$ and $6$

The objective is to select the combination of courses that will maximize the total estimated profit.