\\ Knuth's model for minimizing drum latency time (optimal value 22,996)
\\ Corrected version; modifications wrt the original model are marked by label "corrected"

Minimize
2100 t21 + 44 x2  + 550 t26 -550 t12 + 100 t28  -100 t14  + 100 t30
Subject To
x2 -2z1 <= -2
50 t2 + 1 x3 -2z1  >=  24
x3  -2z2 <= -2
50 t3 -50t2 + x4 -2 z2  >= 5
50 t4 -50 t3  -1 x4  >= 6
50 t5 -50 t4 + x5 >= 15
x5  -2 z3 <= -3
50 t6 -50 t5 + x6 -2 z3  >= 4
x6  -2 z4 <= -2
50 t7 -50 t6 + x4 - 2z4  >= 12
x4 -2 z5  <= 1
50 t8 -50 t7  + x7 -2 z5 >= 35
x7 -2 z6 <= 0
50 t9 -50 t8 + x8 -2 z6  >= 3
50 t10 -50 t9 + x6 -1 x8  >= 10
x6 -2 z7  <= 1
50 t11 -50 t10 + x3 -2 z7  >= 8
50 t12 -50 t11 + x8 -1 x3  >= 3
50 t13 -50 t12 + x9 -2 z8 >= 7
x8 -2 z8  <= 1
50 t13 -50 t12  + x9 + w1 -2 z8  >= 21
x9 + w1 -2 z9  <= 1
50 t14 -50 t13 + x5 -2 z9  >= 35
x5  -2 z10 <= -2
50 t15 -50 t14  + x3 -2 z10  >= 34
50 t16 -50 t15 + x5 -1 x3  >= 6
50 t17 -50 t16 + x9 -2 z3  >= 30

\\ 50 t18 -50 t17  + x4 -2 z9  >= 8 \\ wrong line corrected below
50 t18 -50 t17  + x4 -2 z13  >= 8   \\ corrected line
x9 - 2 z13 <= 1                     \\ corrected line

50 t19 - 50 t18 + x3 -2 z5  >= 34
x3 -2 z11  <= 1
50 t20 -50 t19 -2 z11  >= 9
50 t21 -50 t20 + x2  >= 9
50 t22 -50 t9 + x3 -1 x8  >= 9
50 t23 -50 t22 + x5 -2 z11  >= 8
50 t24 -50 t23 + x4 -1 x5  >= 6
50 t25 -50 t24 + x6 -1 x4  >= 6
50 t26 -50 t25 + x8 -1 x6  >= 3
50 t27 -50 t7 + x7 -2 z5  >= 21
50 t13 -50 t12 + x9 + w2 -2 z8 >= 24
x9 + w2 -2 z12  <= 1
50 t28 -50 t27 + 50 t8 -50 t13 + x5 -2 z12 >= 35
50 t29 -50 t13 -2 z9 >= 15
50 t30 -50 t29 + x2  >= 3
bounds
x2 >= 0
x3 >= 0
x4 >= 0
x5 >= 0
x6 >= 0
x7 >= 0
x8 >= 0
x9 >= 0
t2 >= 0
t3 >= 0
t4 >= 0
t5 >= 0
t6 >= 0
t7 >= 0
t8 >= 0
t9 >= 0
t10 >= 0
t11 >= 0
t12 >= 0
t13 >= 0
t14 >= 0
t15 >= 0
t16 >= 0
t17 >= 0
t18 >= 0
t19 >= 0
t20 >= 0
t21 >= 0
t22 >= 0
t23 >= 0
t24 >= 0
t25 >= 0
t26 >= 0
t27 >= 0
t28 >= 0
t29 >= 0
t30 >= 0
z1 >= 0
z2 >= 0
z3 >= 0
z4 >= 0
z5 >= 0
z6 >= 0
z7 >=0
z8 >= 0
z9 >= 0
z10 >= 0
z11 >= 0
z12 >= 0
z13 >= 0           \\ corrected line
w1 >= 0
w2 >= 0
integers
x2
x3
x4
x5
x6
x7
x8
x9
t2
t3
t4
t5
t6
t7
t8
t9
t10
t11
t12
t13
t14
t15
t16
t17
t18
t19
t20
t21
t22
t23
t24
t25
t26
t27
t28
t29
t30
z1
z2
z3
z4
z5
z6
z7
z8
z9
z10
z11
z12
w1
w2
z13      \\ corrected line
End