MSCI_100_-_10-1_-_Decision_Making_-_exam

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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online