The next four questions are related to the following problem

The next four questions are related to the following problem. Students at Upscale U. are required to take at least 4 humanities and 4 science courses. The maximum allowable number of science course is 12. Each humanities course carries 4 credits and each science course 5 credits. The total number of credits in science and humanities cannot exceed 92. Quality points for each course are assigned in the usual way: the number of credit hours times 4 for an A grade, times 3 for a B grade, and times 2 for a C grade. Lily Cameron expects to get B’s in all her science courses. She expects to get C’s in half her humanities courses, B’s in one-fourth of them, and A’s in the rest. Assuming that she takes x number of humanities courses, and y number of science courses, the goal is to set up a linear programming problem to find a strategy that will maximize her quality points.

(7) What are the constraints of the linear programming problem?

(a) x 4, 4 y 12, 4x + 5y 92 ;

(b) x 4, 4 y 12, 5x + 4y 92 ;

(c) 4x + 5y 92 ;

(d) All of the above ;

What is the objective function for the linear programming problem?

(a) 3x/4 + 3y ;

(b) 13x/4 + 3y ;

(c) 11x/4 + 3y ;

(d) All of the above ;

What is the maximum number of quality points she can possibly get?

(a) 64 ;

(b) 58 ;

(c) 62 ;

(d) All of the above ;

How many courses of each kind should she take in order to earn the maximum possible number of quality points?

(a) 4 humanities, 12 science ;

(b) 18 humanities, 4 science ;

(c) 8 humanities, 12 science ;

(d) All of the above ;

I would ask this multiple times but the questions are all related to that long paragraph.

thanks!

Solution

Let x be the number of Humanities courses
and let y be the number of Science courses

Students are have to take atleast 4 humanities courses
=> x >= 4

and the students are required to take atleast 4 science courses and the number of science courses cannot exceed 12
=> 4 <=y <= 12

each humanities course carries 4 credits and each science course carries 5 credits
and the total number of credits of both these subjects cannot exceed 92 credits
=> 4x + 5y <= 92

=> the corret option for the constraints of the linear programming problem are :

option (A)