SOLUTION: Thuzar’s final exams in college algebra and sociology are scheduled for the same day. She has 12 hours available to study for the two exams. Past experience suggests that each ho

First, Thuzar must satify the condition which is categorical requirement: she must score at least 60 points in the sociology exam.

For it, Thuzar must study sociology for 60/10 = 6 hour, consuming  0.25*6 = 1.5 cups of coffee.


After that, she has remaining 12-6 = 6 hours of the study time and 4-1.5 = 2.5 cups of coffee.


So now Thuzar has the linear minimax problem. It is to find the maximum of the score function

    s(x,y) = 15x + 10y

under these restrictions

        x +     y <= 6          (1)   (hours to study)

     0.5x + 0.25y <= 2.5        (2)   (coffee to drink)

       x >=0,   y >= 0          (3)


where x is hours to study algebra,  y is hours to study sociology.


The restrictions can be presented in this equivalent form

     x + y <= 6

    2x + y <= 10

     x >= 0,  y >= 0.


So the feasibility domain is the quadrilateral in Q1 below the lines  y = 6-x  and  y = 10-2x
with the vertices  (0,0), (0,6), (4,2) and (5,0).


Then easy check shows that the objective function s(x,y) = 15x + 10y  has the maximum value of 15*4 + 10*2 = 80 scores 
at the point (x,y) = (4,2),  giving the ANSWER: 


                  after spending 6 hours to earn 60 points in sociology,

       Thuzar should spent 4 hours for Algebra and 2 additional hours for Sociology.

       Doing this way, she will spend all available 12 hours for studying, will use all available coffee

           and will earn her total combined maximum score of 60 + 80 = 140 points.



       The bottom line answer is:  6+2 = 8 hours for sociology and 4 hours for algebra.