### tp054v1.apm

```Model tp054v1
! Source version 1

! Exact formulation of #54.
! Using IEEE 754 double precision,
! we might be in some trouble here due to
! the fact that the variables, x[i], move
! in different orders of magnitude.
! R.J.Vanderbei and J.D.Hedengren used the y[i]
! instead of the x[i] here as the variables,
! replaced -exp(-(...)/2) by (...),
! simplifying the objective function once more.

Variables
x[1] =     6000    , >=   0, <=     20000
x[2] =        1.5  , >= -10, <=        10
x[3] =  4000000    , >=   0, <=  10000000
x[4] =        2    , >=   0, <=        20
x[5] =        0.003, >=  -1, <=         1
x[6] = 50000000    , >=   0, <= 200000000
obj
End Variables

Intermediates
y[1] = (x[1] - 10000)/8000
y[2] = (x[2] - 1)/1
y[3] = (x[3] - 2000000)/7000000
y[4] = (x[4] - 10)/50
y[5] = (x[5] - 1/1000)*20
y[6] = (x[6] - 100000000)/500000000
h1 = (y[1]^2 + y[1]*y[2]*2/5 + y[2]^2)*25/24
h2 = y[3]^2 + y[4]^2 + y[5]^2 + y[6]^2
mf = -exp(-(h1 + h2)/2)
End Intermediates

Equations
x[1] + 4000*x[2] - 17600 = 0

obj = mf

! best known objective = -exp(-27/280) = -0.9080747577659853
! begin of best known solution
! x[1] = 91600/7 = 13085.71428571429
! x[2] = 79/70 = 1.128571428571429
! x[3] = 2000000
! x[4] = 10
! x[5] = 1/1000 = 0.001
! x[6] = 100000000
! end of best known solution
End Equations
End Model
```

Stephan K.H. Seidl