go this graphically.
horizontal axis: sheets from East side
vertical axis: sheets from West side
Now, a total of 120 sheets are required. Plot the following line:(120,0 and 0,120)
now you have with the axis, an enclosed area, bounded by x=0 (y axis), y=0 (xaxis) y=45, x=45, and the last line you drew. There is a nice theorem that tells you the optimum solution is at one of the cross marks on the bound of this area. So test points 80,40, and 75,45 for total cost.
Notice the points are on the x,y maximum constraint lines.
so if West provides 45, then East provides 75.
lets consider West sending 45 to A: Then East provides 75 to B: total cost to B is .5*45+.40*5+.55*70=63
What if West sent 45 to B?
So, at the point on your graph 75,45 the minimum cost is 55.25.
HOWEVER, there is another point to test, the point (80,40).
consider West sends 40 to A
and what if West sends 40 to B..
so which delivery is mimimum cost?
check my work, please, most of it was done in my head.