Set of inequalities

I would probably treat this like a curve fitting/regression problem.

1) In order to insure the 1st condition is met, solve for one of the variables (eg z=1-x-y) and substitute that into the other equations.
2) Choose a result for each equation about in the middle of each range.
3) Regress for the two unkowns using LINEST().
4) Compute the third variable from the equation derived in (1).
5) Compute each equation and verify that all conditions are met.

This can also be done using Solver, if that fits better into what you are supposed to be learning with this problem.

This is made to order for Solver:

	A	B	C	D	E	F	G	H
1	x	y	z
2	0.0360	0.3819	0.5821
3				Set Cell	to value
4				1.0000	1			D4: =x + y + z
5
6				Constraints	>=	<=
7				0.9651	0.90	1.00		D7: =x + y + 0.94*z
8				0.7323	0.60	0.75		D8: =x + y + 0.54*z
9				0.4718	0.40	0.55		D9: =x + 0.664*y + 0.313*z
10				0.2680	0.20	0.35		D10: =x + 0.26*y + 0.228*z
11				0.1461	0.12	0.22		D11: =0.736*x + 0.176*y + 0.09*z
12				0.0516	0.05	0.10		D12: =0.401*x + 0.05*y + 0.031*z

See http://www.solver.com/learn-how-use-...0-CF21bsfD_BwE or the many other resources on Frontline's web site.

http://www.solver.com/content/basic-...ete-constraint

Those are the decision variables; they can have constraints, but none appear in your original statement.

The solution set is the interior points of some prism ("3D polygon") bounded by all the separating planes formed by those relations.