Question 1181397
<pre>
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</pre>