Start with, what can we do in symbolic form?
symsS G Real
Eq(1) = G > 21;
Eq(2) = S >= 15;
Eq(3) = S <= 18;
Eq(4) = 61 <= 2*S + G;
eq（5）= 2*s + g <= 63;
eq（6）= atand（s/g）> = 30;
Eq(7) = atand(S/G) <= 45;
解决（eq，s，g，'returnconditions',真正的)
There are infinitely many real solutions. So solve cannot handle the problem.
Those inequalities are all just linear though, linear in S and G. Even the case of the atan is linear, sicne over a limited region, the tangent function is monotonic. So we know that if
atand(S/G) <= 45
然后，通过双方的切线，我们不会改变不平等的迹象。告诉我们：
s/g <= 1
或者
S <= G
Likewise, we can infer that
S/G >= sqrt(3/3)
So we have
S >= sqrt(3)/3*G
There is a nice utility called plotregion, that lives on the file exchange for free download. If we represent this linear sytem of inequalities by the matrix A and vector b, where A*x >= b, we might do:
lb = [15 21];% lower bounds on S and G respectively
ub = [18 inf];% upper bounds on S and G
A = [2 1;-2 -1;-1 1;1 -sqrt(3)/3];% linear inequalities
b = [61;-63;0;0];
情节区域（a，b，lb，ub）
XLABEL'S'
ylabel'G'
网格在
That region in the (S,G) plane is where your solutions live. There are infinintely many pairs of real solutions. It looks like Alpha was willing to generate some of them.
If you wish to show the integer solutions, a simple graphical way to do so is to overlay an integer lattice on top of that domain.
[s,g] = meshgrid(16:18,25:30);
hold在
情节（s，g，'ro')
Where you should see the six pairs of integer solutions that live in the solution locus. Five of them lie on the boundary, one is interior.
