The next four questions are related to the following problem. Students at Upscal

Question

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.

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 ;

Explanation / Answer

Here as goal is to maximize the quality points, so if there are total x humanities subjects and y science courses
so their total credits will form the objective function.

So here Z= 2(x/2)+3(x/4)+4(x/4)+ 3y=x+3x/4+x +3y

or Z= 11x/4 +3y

that ist he required objective function.

This is the answer of part (a0

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