EEE 407: Operational Research Second Semester Examination

Operational research paper for the electrical and electronics engineering degree. Establishes the role of operational research in decision making and three components and three advantages of its models, then constructs the dual of a minimisation problem in three variables and determines graphically the range of optimality of the objective coefficients for a two-variable maximisation. Works a production problem through the graphical method: constraint lines, the feasible region, at least two profit lines with the direction of improvement of the objective, the optimal solution, and the equation of any redundant constraint. Solves two-person games, giving the range for the value of the game from a payoff matrix written for the second player and the values of two unknown entries that make a given entry a saddle point. Uses the simplex method on a three-variable maximisation with comment on the significance of the slack variables in the final solution, and minimises an objective under mixed constraints where no variable may fall below twenty. Explains degeneracy and sensitivity analysis, then a two-product mix bounded by sales share, daily raw material availability and usage rates: the optimal product mix, the worth per unit change in the availability of the raw material and its range of applicability, the revenue range over that feasibility range, and the effect of changing the maximum demand for one product by ten units. Closes on proportionality and additivity as the two properties of linear programming models, and on the project network for the construction of a new house from nineteen activities with their predecessors and durations to the critical path.