The log function requires a positive argument, and that implies that each x[i] and y[i] should be positive. But x[2], y[4], and y[8] cannot all be nonnegative, as detected by using the IIS functionality:
con c {i in 1..8}: y[i] >= 0;
solve noobj with lp / iis=on;
expand / iis;
SAS Output
Var x[2] >= 0
Constraint c[4]: y[4] >= 0
Constraint c[8]: y[8] >= 0
Now expand y[4] and y[8]:
expand y[4];
expand y[8];
SAS Output
Impvar y[4] = 1.3573200993*x[4] - 0.2165134044*x[2] - 1.2820512821
Impvar y[8] = - 42.615384615*x[4] - 17.205128205*x[2] - 1.2820512821
Indeed, x[2] >= 0 and y[4] >= 0 together imply x[4] >= 0, which forces y[8] < 0. I would recommend checking your formula for y[8], which should not have all coefficients negative.
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