10.15 Optimal production plan, computer manufacturer. (30 min) 1 Let X = Units of printers, and Y = Units of desktop computers. Objective Maximise total contribution margin of €200X + €100Y Constraints For production line 1: 6X + 4Y < 24 For production line 2: 10X < 20 Sales of X and Y: X − Y < 0 Negative production impossible: X > 0
Y > 0 2 Solution Exhibit 10.15 presents a graphical summary of the relationships. The sales- mix constraint here is somewhat unusual. The X − Y < 0 line is the one going upward at 45° angle from the origin. Using the trial-and-error method: Trial Corner (X; Y) Total contribution margin 1 2 3 4 (0; 0) (2; 2) (2; 3) (0; 6) €200 (0) + €100 (0) = €0 200 (2) + 100 (2) = 600 200 (2) + 100 (3) = 700 200 (0) + 100 (6) = 600 The optimal solution that maximises operating income is two printers and three computers.