EEE 407: Operations Research Second Semester Examination

Operations research paper for the electrical and electronics engineering degree, sat on Tuesday the second of February 2021 from half four to six in the evening, question one compulsory at thirty marks and any two others at twenty. Question one states and explains the characteristics of a good model and two of its limitations, minimises an objective in two variables under three constraints by the graphical method, determines graphically the range of optimality of the objective coefficients for a two-variable maximisation observing the special case where a coefficient may take a zero value, and assigns four salesmen to four clients to maximise profit from a table of profits recorded on previous visits. Question two takes a minimisation under four constraints through the constraint lines, the feasible region, at least two isoprofit lines with the direction of improvement of the objective, the optimal solution and any redundant constraint, and finds the saddle point solution, the pure strategies and the value of a two-player game whose payoffs are written for player B. Question three builds and solves a three-product mix limited by machine hours, by the availability of a special component used singly in two of the products and of a special alloy, and by a trade association agreement to produce no more than fifty units of one product, then allocates five jobs among four fitters from a table of estimated times so as to minimise total time and identify the job that will not be dealt with. Question four states the dual of a maximisation in three variables whose third variable is unrestricted and solves a three-variable maximisation by the simplex method.