Free Essay About Courses Taught

There are two variables to be considered in finding a solution to this problem. One of the variables is the number of undergraduate courses to be taught while the other variable is the number of graduate courses. Let X represent the number of undergraduate courses to be taught by Western College of Business in the fall while Y represents the number of graduate courses to be taught in the fall. From the information offered, the following equations can be made.
X ≥ 30

Y ≥ 20

The two equations above relate to the number of graduate courses that can be offered. With regards to the faculty requirements for the number of courses, the following equation can be used to express the relationship between the variables
X + Y ≥ 60
It is important to note that in this relationship, X ≥ 30 and Y ≥ 20. Based on the information given, another equation expressing the total faculty salaries for the undergraduate and graduate courses can also be expressed as shown below:
Total faculty salaries = 2500X + 3000Y

At the minimum, the following are the faculty salaries:

= 2500(30) + 3000(20)
= 75000 + 60000
= 135000 for fifty courses.
However, there is a contract requirement that sixty courses are offered in the college. This implies that there are ten more courses above the minimum total requirement for both undergraduate and graduate courses. Given that the undergraduate courses contribute the least amount to the total faculty salaries, the ten extra courses should be undergraduate courses so that the total faculty salaries can remain at a minimum.
Total faculty salaries = 2500X + 3000Y
When there is an equal distribution of the courses, (2500 * 30) + (3000 * 30) = 165,000. When there are 40 undergraduate courses and 20 graduate courses, the total faculty salaries are (2500 * 40) + (20*3000) = 160,000. As such, the solution that offers the minimum faculty salaries is a combination of forty undergraduate courses and twenty graduate courses. This can be used in organizations for quantitative analysis in order to determine the options that carry the least cost of production (Szabo, 2000).

References

Szabo, F. (2000). Linear algebra: An introduction using Mathematica. San Diego. Harcourt, Acad. Press.