The short answer is no. Solve will do sets of linear and non-linear equations, but not with constraints as you want. MS handles inequalities, but not in solutions of equations. What you need is probably Simplex or a Simplex like function. MS is perfectly capable of handling a Simplex code. You'd just need to write it or port it.
Having said that, you can sort of get what you want graphically using plot and parametric plot. Tedious, but it may be all you need.
I plotted the y constraints in red and the x constraints in blue. The line was plotted in orange and I added the shading as a guide. You can then find the values in the plot and test them against the cost function.