SOLUTION: Professor Weejohs teaches two sections of business analytics, which combined will result in 120 final exams to be graded. Professor Weejohs has two assistants, Ralph and Melanie, w

Question 1181397: Professor Weejohs teaches two sections of business analytics, which combined will result in 120 final exams to be graded. Professor Weejohs has two assistants, Ralph and Melanie, who will grade the final exams. There is a 3-day period between the time the exam is administered and when final grades must be posted. During this period Ralph has 12 hours available and Melanie has 10 hours available to grade the exams. It takes Ralph an average of 7.2 minutes to grade an exam, and it takes Melanie 12 minutes to grade an exam; however, Ralph’s exams will have errors that will require Professor Weejohs to ultimately regrade 10% of the exams, while only 6% of Melanie’s exams will require regrading. Professor Weejohs wants to know how many exams to assign to each assistant to grade in order to minimize the number of exams to regrade.
Answer by mccravyedwin(407) (Show Source): You can put this solution on YOUR website!

Let x be the number of exams to assign Melanie.
Then since there are 120 exams, Ralph will be assigned 120-x.

Inequality for Melanie's grading time: 12x minutes = 0.2x hours,
which must be less than or equal to 10 hours, or

0.2x <= 10
   x <= 50   

Inequality for Ralph's grading time: 7.2(120-x) minutes = 0.12(120-x) hours,
which must be less than or equal to 12 hours, or

0.12(120-x) <= 12
      120-x <= 100
         -x <= -20
          x >= 20

So  20 <= x <= 50

We want to minimize 

C = 0.06x + 0.10(120-x) = 0.06x + 12 - 0.10x = 12.06 - 0.04x,

which will be when we choose x = 50 (in order to subtract the most from 12.06.)

So the Professor will assign 50 exams to Melanie and the other 120-50=70 to
Ralph so that the professor will only need to re-grade 10.06 (about 10) exams.

Answer: The professor should assign 50 exams to Melanie and the other 70 to Ralph.

Edwin

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