Let X be the number of counselors, and
let Y be the number of aides.


Then the Cost function is 

C(X,Y) = 2400*X + 1100*Y,    (1)


and they want you minimize it under these constraints:


X + Y <= 35,      (2)     ("The camp can accommodate up to 35 staff members")

X + Y >= 20       (3)     ("The camp . . /.  needs at least 20 to run properly")

Y >= 10           (4)     ("They must have at least 10 aides")

Y <=         (5)     ("They . . . may have up to 3 aides for every 2 counselors. ")

X >= 0,  Y >= 0.  (6)


The feasible domain is shown below. It is the quadrilateral in quadrant I constrained by the red, green, blue and purple lines.





Lines X+Y = 35 (red), X+Y = 20 (green), Y = 10 (blue), Y =  (purple)


Find the vertices of this quadrilateral as intersections of the given lines
(by solving the corresponding system of equations for each vertex).


Then use the Linear Programming method.

The method says: 

    To find the minimum, calculate the function F(X,Y) at the vertices of the polygon (at the vertices of the quadrilateral, in this case !)

    and select that vertex where the function is minimal.