A professor needs help from three student helpers to complete four tasks. The first task is grading; the second is scanning; the third is copying, and the fourth is organizing student portfolios. The estimated time for each student to do each task is given in the matrix below.
$$\begin{array} { r r r r r }
& \mathbf { 1 } & \mathbf { 2 } & \mathbf { 3 } & \mathbf { 4 } \
\hline \text { Student A } & 90 & 50 & 40 & 20 \
\mathbf { B } & 120 & 60 & 30 & 50 \
\mathbf { C } & 110 & 60 & 50 & 70 \
\hline
\end{array}$$
-Which of the following constraints represents the assignment for student A?
A) XA1 +XA2 + XA3 + XA4 = 0
B) XA1 +XA2 + XA3 + XA4 = 1
C) XA1 +XA2 + XA3 + XA4 ? 1
D) XA1 +XA2 + XA3 + XA4 ? 0

Question

A professor needs help from three student helpers to complete four tasks. The first task is grading; the second is scanning; the third is copying, and the fourth is organizing student portfolios. The estimated time for each student to do each task is given in the matrix below.
 $$\begin{array} { r r r r r } 
& \mathbf { 1 } & \mathbf { 2 } & \mathbf { 3 } & \mathbf { 4 } \
\hline \text { Student A } & 90 & 50 & 40 & 20 \
\mathbf { B } & 120 & 60 & 30 & 50 \
\mathbf { C } & 110 & 60 & 50 & 70 \
\hline
\end{array}$$
-Which of the following constraints represents the assignment for student A?
A) XA1 +XA2 + XA3 + XA4 = 0
B) XA1 +XA2 + XA3 + XA4 = 1
C) XA1 +XA2 + XA3 + XA4 ? 1
D) XA1 +XA2 + XA3 + XA4 ? 0

Quizplus · Accepted Answer

The constraint for student A represents that exactly one task must be assigned to student A, hence the sum of the variables (each representing whether a task is assigned to student A) equals 1.

A Professor Needs Help from Three Student Helpers to Complete