12 – 1
Chapter 12
Advanced Optimization Applications
Case Problem: CAFE Compliance in the Auto Industry
1. The model is
! PASSENGR CAR MILES PER GALLON;
PASSMPG = 30;
PCOST = 15;
TCOST = 17;
MAX = PD*(PP – PCOST) + TD*(TP – TCOST);
The objective function
PD*(PP – PCOST) + TD*(TP – TCOST)
is the desired contribution margin.
2. The LINGO solution to the above model is
Variable Value Reduced Cost
PASSMPG 30.00000 0.000000
LTRUCKMPG 20.00000 0.000000
PD 225.0000 0.000000
PP 26.25000 0.000000
Chapter 12
12 –
2
Row Slack or Surplus Dual Price
1 0.000000 0.000000
2 0.000000 0.000000
3 0.000000 11.25000
3. As seen from the LINGO solution in question 2, 225 passenger cars are sold and 270.5 light trucks are sold.
4. See Figure 12.14.
5. The Café average is
and
CAFEAVG > 25;
to the LINGO model gives
Local optimal solution found.
Objective value: 6274.514
Extended solver steps: 5
Total solver iterations: 39
Variable Value Reduced Cost
PASSMPG 30.00000 0.000000
Row Slack or Surplus Dual Price
1 0.000000 296.9150
2 0.000000 445.3716
3 0.000000 14.35300
4 0.000000 11.25726
5 0.000000 –287.0601