EXPLICIT SOLVABILITY OF A CLASS OF INFINITE LINEAR ECONOMIC-MODELS

Let X(1) and X(2) be partially ordered real Banach spaces, f, g is an element of X(1) with f less than or equal to g, q, r is an element of X(2), with q less than or equal to r, phi(1) is an element of X(1)*, phi(2) is an element of X(2)* B : X(1) --> X(2) be a bounded linear map and C:X(2)--> X(2) be a bounded invertible linear map. Consider the following infinite linear programming problem: Maximize phi 1 (x) + phi(2) (y) subject to f less than or equal to x less than or equal to g and q less than or equal to Bx + Cy less than or equal to r. In this paper we study conditions under which this problem is explicitly solvable. We also show that this result can be applied to solve a class of continuous production-planning and input-output models.