@vv While I don't see any nice way to get Maple to solve even the reduced 2-dimensional problem (once **x3** is eliminated), for fun here are Yet More Ways to get some plots out of Maple.

Here's a quick way, using the reduced system (without **floor**) cited as coming from Mma. I transform a 2-d plot using the isolated formula for **x3**, since **implicitplot3d** won't find any data on right on the plane.

restart;
# using the cited solution from Mma
eqs:=(155/2 < x1 and x1 < 78 and 744/7-4*x1*(1/7) < x2 and x2 < 62 or
72 <= x1 and x1 <= 73 and 102-4*x1*(1/7) < x2 and x2 < 62 or 73 < x1 and x1 <= 147/2 and
102-4*x1*(1/7) < x2 and x2 <= 726/7-4*x1*(1/7) or 147/2 < x1 and x1 < 74 and 60 <= x2 and
x2 <= 726/7-4*x1*(1/7) or 74 <= x1 and x1 < 75 and 726/7-4*x1*(1/7) < x2 and x2 < 62 or
153/2 < x1 and x1 < 78 and 726/7-4*x1*(1/7) < x2 and x2 < 60 or x1 = 72 and 58 <= x2 and
x2 < 60 or 72 < x1 and x1 < 74 and 58 <= x2 and x2 <= 708/7-4*x1*(1/7) or 75 <= x1 and
x1 < 76 and 102-4*x1*(1/7) < x2 and x2 < 60 or x1 = 74 and 442/7 < x2 and x2 < 64 or
74 < x1 and x1 < 75 and 738/7-4*x1*(1/7) < x2 and x2 <= 744/7-4*x1*(1/7) or 74 <= x1 and
x1 < 75 and 708/7-4*x1*(1/7) < x2 and x2 <= 102-4*x1*(1/7) or 151/2 < x1 and x1 < 76 and
708/7-4*x1*(1/7) < x2 and x2 < 58 or 157/2 < x1 and x1 < 80 and 762/7-4*x1*(1/7) < x2 and
x2 < 64 or 68 <= x1 and x1 < 137/2 and 56 <= x2 and x2 <= 666/7-4*x1*(1/7) or x1 = 137/2 and
x2 = 56 or x1 = 70 and 56 < x2 and x2 < 58 or 70 < x1 and x1 <= 71 and 56 <= x2 and x2 < 58 or
71 < x1 and x1 < 72 and 56 <= x2 and x2 <= 690/7-4*x1*(1/7) or 70 <= x1 and x1 <= 281/4 and
54 <= x2 and x2 < 55 or 281/4 < x1 and x1 < 72 and 54 <= x2 and x2 <= 666/7-4*x1*(1/7)):
P2d:=plots:-inequal(eqs, x1=0..100, x2=0..100, nolines,
view=[default,default]):
P2d;

plottools:-transform((x1,x2)->[x1,x2,1-2*x1*(1/3)-7*x2*(1/6)])(P2d):
plots:-display(%,lightmodel=none,orientation=[80,50,0]);

Working with the original system involving floor, a 2-d implicit plot can be produced using the **implicitplot** command. It can find the complementary set more robustly (if the ranges and grid size vary) but the resolution seems poor unless it is refined so much that it takes a while to compute. Computing the set as below is quick, but seems prone to miss portions unless the ranges/grid are "just right".

foo:={4*x1+7*x2+6*x3 = 186,
floor((1/2)*x1)+floor((1/5)*x2)+floor((1/3)*x3) = 18,
floor((1/5)*x1)+floor((1/2)*x2)+floor((1/4)*x3) = 21}:
px3:=solve(4*x1+7*x2+6*x3 = 186, {x3}):
new:=remove(`=`,map(rhs-lhs,eval(foo,px3)),0):
# seems tricky to ensure that all the region is found
P2d:=plots:-implicitplot(unapply((`or`(op(map(u->u>0 or u<0,new)))),[x1,x2]),
50..100,50..100,grid=[151,151],gridrefine=1):
P2d;

plottools:-transform((x1,x2)->[x1,x2,1-2*x1*(1/3)-7*x2*(1/6)])(P2d):
plots:-display(%,lightmodel=none,orientation=[80,50,0]);

It's a shame that **solve** knows little about floor/ceil/frac.