Question

A student has up to 12 hours of study time in preparing for his final exams for four courses. Without preparation, the student is projected to get 3.0 for Course A, 3.0 for Course B, 2.7 for Course C, and 2.7 for Course D. Due to varying difficulty and personal familiarity levels with course content, for each hour of study, the projected GPA improvement is 0.3 for Course A, 0.25 for Course B, 0.2 for Course C and 0.15 for Course D. If the student would like to make sure that no individual course should receive a GPA below 3.3, study time is allocated by incremental of full hours, and understand that the maximum GPA for each course is 4.0 regardless extra study time. How should the student allocate study time to maximize overall semester GPA? Assuming four courses are of the same weight in calculating overall semester GPA.

Q14. What is the highest possible semester GPA the student can achieve based on your Solver solutions (keep or rounded to two decimals if necessary)

Answer 1

Let

Hj = Hours devoted to course-j for j=A, B, C, D

Maximize Z = (1/4)*(3 + 0.3 HA + 3 + 0.25 HB + 2.7 + 0.2 HC + 2.7 + 0.15 HD) =(1/4)*(0.3 HA + 0.25 HB + 0.2 HC + 0.15 HD + 11.4)

Subject to,

HA + HB + HC + HD <= 12

3.0 + 0.30 HA >= 3.3 or, 0.30 HA >= 0.3
3.0 + 0.25 HB >= 3.3 or, 0.25 HB >= 0.3
2.7 + 0.20 HC >= 3.3 or, 0.20 HC >= 0.6
2.7 + 0.15 HD >= 3.3 or, 0.15 HD >= 0.6

3.0 + 0.30 HA <= 4.0 or, 0.30 HA <= 1.0
3.0 + 0.25 HB <= 4.0 or, 0.25 HB <= 1.0
2.7 + 0.20 HC <= 4.0 or, 0.20 HC <= 1.3
2.7 + 0.15 HD <= 4.0 or, 0.15 HD <= 1.3

Excel formulation:

Solver inputs:

Solution:

	HA	HB	HC	HD
Value of	3.33	1.67	3.00	4.00
Overall GPA	0.075	0.0625	0.05	0.0375	3.50
s.t.
Min GPA in A	0.3				1	>=	0.3
Min GPA in B		0.25			0.42	>=	0.3
Min GPA in C			0.2		0.6	>=	0.6
Min GPA in D				0.15	0.6	>=	0.6
Max GPA in A	0.3				1	<=	1.0
Max GPA in B		0.25			0.42	<=	1.0
Max GPA in C			0.2		0.6	<=	1.3
Max GPA in D				0.15	0.6	<=	1.3
Total hrs.	1	1	1	1	12	<=	12

Highest possible GPA = 3.50