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A more efficient method of locating the optimum of a second order response function was of interest in this work. In order to do this, the principles of optimal designs of experiment is invoked and used for this purpose. At the end, it was discovered that the noticeable pitfall in response surface methodology (RSM) was circumvented by this method as the step length was obtained by taking the derivative of the response function rather than doing so by intuition or trial and error as is the case in RSM. A numerical illustration shows that this method is suitable for obtaining the desired optimizer in just one move which compares favourably with other known methods such as Newton-Raphson method which requires more than one iteration to reach the optimizer.

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This work has successfully shown that the optimum of a quadratic response function with zero coefficients except that of the quadratic term lies at the origin. This was achieved by using optimal designs technique for solving unconstrained optimization problems with quadratic surfaces. In just one move, the objective of the work, that is, x min = 0 was realized.

Performance measures and waiting time cost for higher priority patients with severe cases over lower priority patients with stable cases using preemptive priority queuing model were obtained. Also, a total expected waiting time cost per unit time for service and the expected service cost per unit time for priority queuing models: M/M/2: ∞/NPP and M/M/2: ∞/PP were respectively formulated and optimized to obtain optimum cost service rate that minimizes the total cost. The results were applied to obtain optimum service rate that minimizes the total cost of providing and waiting for service at the emergency consulting unit of hospital.