Decision-making of almost any kind can be framed as an optimisation problem, falling into one of two broad families: constrained or unconstrained. Building on this framework, the present paper develops a Steepest Descent (SD) algorithm and a Conjugate Gradient (CG) algorithm, both constructed around a newly proposed parameter, beta k itself. To evaluate their performance, both algorithms are implemented in MATLAB and tested on a set of nonlinear unconstrained test functions that have not previously appeared in the literature for this problem's numerical examples, ensuring an independent assessment of their behavior. The paper's central contribution is beta k, proposed specifically to make the CG algorithm more effective at locating the minimum of the objective function. Wherever it appears below, beta k denotes this new parameter, and all results obtained using it are compared directly against those of the classical SD algorithm, allowing for a clear, side-by-side evaluation of efficiency and convergence behavior. Across the MATLAB experiments, performance was tracked along two key dimensions: accuracy of the final solution and running time required to reach it. The results show that the SD algorithm consistently needed more iterations to converge than the CG algorithm equipped with the new beta k, which reached the solution more efficiently while maintaining a runtime close to that of SD. This combination of faster convergence and comparable computational cost suggests that the new parameter offers a genuine practical advantage rather than a trade-off. These results point toward the possibility of tackling larger, more complex unconstrained problems involving additional variables, and lay the groundwork for extending the proposed approach to broader classes of optimisation problems in future work.