Question

Dr. Lum teaches part-time at two community colleges, Hilltop College and Serra College. Dr. Lum can teach up to 5 classes per semester. For every class he teaches at Hilltop College, he needs to spend 3 hours per week preparing lessons and grading papers. For each class at Serra College, he must do 4 hours of work per week. He has determined that he cannot spend more than 18 hours per week preparing lessons and grading papers. If he earns $6,000 per class at Hilltop College and $7,500 per class at Serra College, how many classes should he teach at each college to maximize his income, and what will be his income?

To maximize his income, Dr. Lum should teach_______classes for Hilltop College and __________classes for Serra College. His maximum income would be________.

Answer 1

z (max) = 34500 $

x₁ = 2

x₂ = 3

Explanation:

Hilltop College

3 hours per week preparing lessons and grading papers

Serra College

4 hours per week preparing lessons and grading papers

Total hours to spend per week preparing lessons 18

Let´s call x₁ numbers of class at Hilltop College

and x₂ numbers of class at Serra College then:

Objective function

z = 6000*x₁ + 7500*x₂

Constraints:

1.- x₁ + x₂ ≤ 5 the total number of class

2.- 3*x₁ + 4*x₂ ≤ 18

3. General constraints x₁ ≥ 0 x₂ ≥ 0 integers

After 6 iteration optimal solution is: From on-line solver

z (max) = 34500 $

x₁ = 2

x₂ = 3