Overlaying 2d plots of regions with different colors and labels

Question

I'm using the command Show to overlay the following three regions:

---

r1 = RegionPlot[ 5/2 y + 3 x <= 3 && y < 2/3 && 5/2 y + x <= 2, {x, 0, 1}, {y, 0, 1}]

r2 = RegionPlot[ y < 13/12 - 13/12 x && y < 13/24 , {x, 0, 1}, {y, 0, 1}]

r3 = RegionPlot[y <= 1 - x && y < 2/3 , {x, 0, 1}, {y, 0, 1}]

Show[r1, r2, r3]

---

The problem is that I can't label them in the final picture and I'd like to change the colors as well to distinguish them more clearly. If possible, I'd like to plot some special points on this picture (like a few of the corners). Is there a "simple" way of doing that?

I'd appreciate any input that you may have. Thanks!

Answer 1

Something like this?

r1 = RegionPlot[
   5/2 y + 3 x <= 3 && y < 2/3 && 5/2 y + x <= 2, {x, 0, 1}, {y, 0, 
    1}, PlotStyle -> {Opacity[0.2], Yellow}, 
   PlotLabels -> Placed["First region", {.8, .3}]];
r2 = RegionPlot[
   y < 13/12 - 13/12 x && y < 13/24, {x, 0, 1}, {y, 0, 1}, 
   PlotStyle -> {Opacity[0.3], Green}, 
   PlotLabels -> Placed["Second region", {.4, .4}]];
r3 = RegionPlot[y <= 1 - x && y < 2/3, {x, 0, 1}, {y, 0, 1}, 
   PlotStyle -> {Opacity[0.5], LightRed}, 
   PlotLabels -> Placed["Third region", {.2, .7}]];
Overlay[{r1, r2, r3}]

Answer 2

{a, b, c} = {5/2 y + 3 x <= 3 && y < 2/3 && 5/2 y + x <= 2, 
   y < 13/12 - 13/12 x && y < 13/24, y <= 1 - x && y < 2/3};
RegionPlot[{
  Callout[a, "a corner", {1/2, 3/5} + {.1, 0.3}, {1/2, 3/5}, 
   CalloutMarker -> "Arrow", Background -> Blue, 
   LabelStyle -> White],
  Callout[b, "b", {0.2, 13/24} + {0, 0.3}, {0.2, 13/24}, 
   CalloutMarker -> "Arrow"], 
  Callout[b, "b corner", {1/2, 13/24} + 0.3, {1/2, 13/24}, 
   Appearance -> "Balloon", Background -> Green, LabelStyle -> Gray],
  Callout[c, "c", Appearance -> "Arrow", Background -> Red, 
   LabelStyle -> White]
  },
 {x, 0, 1}, {y, 0, 1}]