Filling between more than two boundaries

Here is a simple example of what I am trying to do; fill the area described by the three inequalities:

$$ y le 11 + x label{1} tag{1}$$
$$ y le 27 – x tag{2}$$
$$ y le frac{1}{5}(90 – 2x) tag{3}$$

I have so far:

Plot[{11 + x, 27 - x, 1/5 (90 - 2 x)}, {x, 0, 20}, 
    Filling -> {2 -> {{3}, {White, LightBlue}}}]

Which produces:

My question is how to add multiple constraints on an area in general — so for this specific question add the constraint specified by equation $eqref{1}$.

r = ImplicitRegion[
   y <= 11 + x && y <= 27 - x && y <= 1/5 (90 - 2 x) && x >= 0 && 
    y >= 0, {x, y}];
Show[Plot[{11 + x, 27 - x, 1/5 (90 - 2 x)}, {x, 0, 20}, 
  AxesOrigin -> {0, 0}], RegionPlot[r]]

Plot[{11 + x, 27 - x, 1/5 (90 - 2 x)}, {x, 0, 20}, PlotPoints -> 40, 
 Filling -> {3 -> {Axis, {None, Blue}}, 2 -> {{3}, {White, None}}, 
   1 -> {{3}, {White, None}}}]

Plot[{11 + x, 27 - x, 1/5 (90 - 2 x), Min[11 + x, 27 - x], 
  Min[11 + x, 27 - x, 1/5 (90 - 2 x)]}, {x, 0, 20}, 
 Filling -> {5 -> {Axis, {White, LightBlue}}, 4 -> {{3}, {None, Yellow}}}]