By using an exterior penalty function and recent boundedness and existence results for monotone complementarity problems, we give existence and boundedness results, for a pair of dual convex programs, of the following nature. If there exists a point which is feasible for the primal problem and which is interior to the constraints of the Wolfe dual, then the primal problem has a solution which is easily bounded in terms of the feasible point. Furthermore there exists no duality gap. We also show that by solving an exterior penalty problem for only two values of the penalty parameter we obtain an optimal point which is approximately feasible to any desired preassigned tolerance. This result is then employed to obtain an estimate of the perturbation parameter for a linear program which allows us to solve the linear program to any preassigned accuracy by an iterative scheme such as a successive over-relaxation (SOR) method.