We have three jobs $(1,2,3)$ and four machines $(1,2,3,4).$ Each machine can do any of the three jobs, and a job can be assigned to any of the four machines. We wish to assign our three jobs to machines to minimize total cost.

Let Xij $=1$ if job i is assigned to machine j$,$ and Xij $=0$ if not.

What is the constraint associated with machine $3$ for the above assignment problem?

Question $4$ options:

a$)$ x$13+$ x$23+$x$33=1$

b$)$ x$31+$ x$32+$x$33+$x$34=1$

c$)$ x$31+$ x$32+$x$33+$x$34<=1$

d$)$ x$13+$ x$23+$x$33<=1$

e$)$ x$11+$ x$12+$x$13+$x$14=1$