Question

how many faculty of each rank should be hired at each college to exactly meet the demand for sections and completely exhaust the salary budget
Rank
table. Lecture. Instrutor
Section taught. 3. 4
annual salary. 20. 25
(Thousands $)

Table. Community college
1. 2. 3
demand for sec. 30. 33. 35
Salary budget. 200. 210. 220
(Thousand$)

I don't understand how to set up to solve

Answer 1

Lecturer: teaches 3 sections for $20K
Instructor: teaches 4 sections for $25K
For each college, assume we hire
t=number of teachers,
i=number of instructors,
then if we were to satisfy requirements and spend all the budget, then
20t/3+25i/4 = budget
or
80t+75i=12*budget ...(1)
where t and i are integers.
For simple cases like these, the resulting diophantine equation (1) can be solved by trial and error or by more rigorous means, depending on the requirements of your teacher.

Answer 2

can someone explain what to do next?