I have a very simple question that i'm struggling to answer:
A border crossing is staffed 24/7 and supervision is covered by 3 separate shifts; morning, afternoon and night. The number of border agents on each shift is never greater than 15. The average number of border agents is 13. what is the ratio of agents per shift given that:
- There are equal numbers of agents on the morning and afternoon shift
- The shift with the greatest number of agents is the night shift
This is my attempted solution:
(x + y + z)/3 = 13 and x=y
Hence (2x + z)/3=13 and z = 39 - 2x
This is as far as i've been able to get.
Any help with details of what i'm missing would be greatly appreciated!
all the best
Sebastian
You've gotten as far as you can get with the algebra and equations. Now you have to use the information that $x,z\le 15$. In particular, $$z = 39-2x \ge 39-2\cdot 15 = 9.$$ So if $x=y=15$, you get $z=9$. If $x=y=14$, you get $z=11$, and if $x=y=13$, you get $z=13$. And, lastly, if $x=y=12$, then $z=15$. Is this it?