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M=c/4
R = (c-M)/3
B = (c-M-R)/2
P = 16
c = M+R+B+P
x = M+R

4M-c = 0
M+3R-c = 0
2B+M+R-c = 0
P = 16
B+M+P+R-c = 0
M+R-x = 0

Pivot: Row 1 ↔ Row 3
2B+M+R-c = 0
M+3R-c = 0
4M-c = 0
P = 16
B+M+P+R-c = 0
M+R-x = 0

Row 5 - 1/2 · Row 1 → Row 5
2B+M+R-c = 0
M+3R-c = 0
4M-c = 0
P = 16
0.5M+P+0.5R-0.5c = 0
M+R-x = 0

Pivot: Row 2 ↔ Row 3
2B+M+R-c = 0
4M-c = 0
M+3R-c = 0
P = 16
0.5M+P+0.5R-0.5c = 0
M+R-x = 0

Row 3 - 1/4 · Row 2 → Row 3
2B+M+R-c = 0
4M-c = 0
3R-0.75c = 0
P = 16
0.5M+P+0.5R-0.5c = 0
M+R-x = 0

Row 5 - 0.5/4 · Row 2 → Row 5
2B+M+R-c = 0
4M-c = 0
3R-0.75c = 0
P = 16
P+0.5R-0.375c = 0
M+R-x = 0

Row 6 - 1/4 · Row 2 → Row 6
2B+M+R-c = 0
4M-c = 0
3R-0.75c = 0
P = 16
P+0.5R-0.375c = 0
R+0.25c-x = 0

Pivot: Row 3 ↔ Row 4
2B+M+R-c = 0
4M-c = 0
P = 16
3R-0.75c = 0
P+0.5R-0.375c = 0
R+0.25c-x = 0

Row 5 - Row 3 → Row 5
2B+M+R-c = 0
4M-c = 0
P = 16
3R-0.75c = 0
0.5R-0.375c = -16
R+0.25c-x = 0

Row 5 - 0.5/3 · Row 4 → Row 5
2B+M+R-c = 0
4M-c = 0
P = 16
3R-0.75c = 0
-0.25c = -16
R+0.25c-x = 0

Row 6 - 1/3 · Row 4 → Row 6
2B+M+R-c = 0
4M-c = 0
P = 16
3R-0.75c = 0
-0.25c = -16
0.5c-x = 0

Pivot: Row 5 ↔ Row 6
2B+M+R-c = 0
4M-c = 0
P = 16
3R-0.75c = 0
0.5c-x = 0
-0.25c = -16

Row 6 - -0.25/0.5 · Row 5 → Row 6
2B+M+R-c = 0
4M-c = 0
P = 16
3R-0.75c = 0
0.5c-x = 0
-0.5x = -16


x = -16/-0.5 = 32
c = 0+x/0.5 = 0+32/0.5 = 64
R = 0+0.75c/3 = 0+0.75 · 64/3 = 16
P = 16/1 = 16
M = 0+c/4 = 0+64/4 = 16
B = 0-M-R+c/2 = 0-16-16+64/2 = 16

B = 16
M = 16
P = 16
R = 16
c = 64
x = 32

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