Maple calculations

with(simplex);

A3 := 8*a + 12*b + 6*c + d;

A4 := 16*a+32*b+24*c+8*d+e;

A5 := 32*a+80*b+80*c+40*d+10*e+f;

A6 := 64*a+192*b+240*c+160*d+60*e+12*f+g;

A7 := 128*a+448*b+672*c+560*d+280*e+84*f+14*g+h;

X1 := [2*a+b <= 2];

X2 := [4*a+2*b+c <= 4, 2*a+c <= 2, 2*b+c <= 2, c <= 1];

X3 := [op(X2), op(subs([a=b,b=c,c=d],X2)), 8*a+6*b+6*c+2*d<=11, 4*a+4*b+3*c+d<=6, 7*a+3*b+3*c+d <= 7, 4*a+6*c+2*d<=7, 6*a+3*c+d<=5, 2*a+d <= 2];

X4 := [op(X3), op(subs([a=b,b=c,c=d,d=e],X3)), op(subs([b=c,c=e],X2)),A4 <= 43];

X5 := [op(X4), op(subs([a=b,b=c,c=d,d=e,e=f],X4)), 2*a+f <= 2, A5 <= 124];

X6 := [op(X5), op(subs([a=b,b=c,c=d,d=e,e=f,f=g],X5)), op(subs([b=d,c=g],X2)), op(subs([b=c,c=e,d=g],X3))];

evalf(subs(maximize(A6,X6,NONNEGATIVE),A6));

364.6984127

evalf(subs(maximize(A6,X6,NONNEGATIVE),[64*a,192*b,240*c,160*d,60*e,12*f,g]));

[29.81627297, 98.26771654, 128.5039370, 77.27034121, 21.73228346, 8.409448819, 0.]

evalf(subs(maximize(A6,[op(X6),g=1],NONNEGATIVE),A6));

355

X6 := [op(X6), A6 <= 364];

X7 := [op(X6), op(subs([a=b,b=c,c=d,d=e,e=f,f=g,g=h],X6)), 2*a+h <= 2];

evalf(subs(maximize(A7,X7,NONNEGATIVE),A7));

1092