MSCI_100_-_10-1_-_Decision_Making_-_exam - Introduction to...

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Introduction to Decision Modeling: Examples and Solution methods Linear Programming Example: Bearskin Airlines is considering adding daily flights to Calgary and Halifax from Waterloo Region Airport. The airport has 1 gate, which operates 12 hours/day, and each flight requires 1 hour of gate time. Each Calgary flight requires 15 hours of crew time and will earn $2500 profit. Each Halifax flight requires 10 hours of crew time and will earn $2000 profit. Total crew time is limited to 150 hours/day. The demand for Calgary flights is no more than 9 flights per day. If Bearskin wishes to maximize profits, how many daily Calgary & Halifax flights should be added? Steps for the graphical solution: (This procedure only works for problems with 2 variables. More complex problems require use of the “simplex method” – not covered in our course) 1) Define the objective function: -We wish to maximize profits Z -Let x C = number of daily flights to Calgary; each flight earns $2500 -Let x H = number of daily flights to Halifax; each flight earns $2000 Objective function: Maximize Z = 2500x C + 2000x H 2) Define constraints: -Gate capacity: x C + x H 12 -Labour/crew time 15x C + 10x H 150 -Market demand for Calgary x C 9 -Non-negativity x C 0, x H 0 3) Graph each constraint to identify the feasible region -Treat the inequalities as equations; plot the lines; identify which side of the line is feasible (and which is not feasible) -Together the constraint lines mark off the feasible region 4) Draw 1 or more “iso-profit” lines through the feasible region to identify the optimal solution (i.e., the x C , x H values corresponding with maximum profit.) -Select a convenient (x C , x H ) point near the feasible region; determine the corresponding value of Z; then find another point with the same Z value to draw an iso-profit line. -Note: optimal result always occurs at a point of intersection of two constraint lines (or if
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MSCI_100_-_10-1_-_Decision_Making_-_exam - Introduction to...

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