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Objective Coefficient Ranges

1. The Diet Problem

LINGO model:

MODEL:

SETS:

FOODS/ BREAD, MEAT, VEGGIES/

:CALORIES, COST, VITAMINS, QUANTITY;

ENDSETS

DATA:

CALORIES= 24, 32, 16;

COST= 2, 3, 2;

VITAMINS= 8, 20, 12;

CALORIE_UPPER = 450;

CALORIE_LOWER = 200;

VITAMIN_LOWER = 100;

ENDDATA

!Objective function;

MIN= @SUM(FOODS: QUANTITY*COST);

@SUM(FOODS: QUANTITY*CALORIES) <= CALORIE_UPPER; !Upper limit of calories;

@SUM(FOODS: QUANTITY*CALORIES) >= CALORIE_LOWER; !Lower limit of calories;

@SUM(FOODS: QUANTITY*VITAMINS) >= VITAMIN_LOWER; !Lower limit of vitamins;

END

Global optimal solution found.

Objective value: 17.85714

Infeasibilities: 0.000000

Total solver iterations: 2

Variable Value Reduced Cost

CALORIE_UPPER 450.0000 0.000000

CALORIE_LOWER 200.0000 0.000000

VITAMIN_LOWER 100.0000 0.000000

CALORIES( BREAD) 24.00000 0.000000

CALORIES( MEAT) 32.00000 0.000000

CALORIES( VEGGIES) 16.00000 0.000000

COST( BREAD) 2.000000 0.000000

COST( MEAT) 3.000000 0.000000

COST( VEGGIES) 2.000000 0.000000

VITAMINS( BREAD) 8.000000 0.000000

VITAMINS( MEAT) 20.00000 0.000000

VITAMINS( VEGGIES) 12.00000 0.000000

QUANTITY( BREAD) 3.571429 0.000000

QUANTITY( MEAT) 3.571429 0.000000

QUANTITY( VEGGIES) 0.000000 0.4285714

Row Slack or Surplus Dual Price

OBJ 17.85714 -1.000000

2 250.0000 0.000000

3 0.000000 -0.7142857E-01

4 0.000000 -0.3571429E-01

Ranges in which the basis is unchanged:

Objective Coefficient Ranges

Current Allowable Allowable

Variable Coefficient Increase Decrease

QUANTITY( BREAD) 2.000000 0.2500000 0.8000000

QUANTITY( MEAT) 3.000000 0.6000000 0.3333333

QUANTITY( VEGGIES) 2.000000 INFINITY 0.4285714

Righthand Side Ranges

Row Current Allowable Allowable

RHS Increase Decrease

2 450.0000 INFINITY 250.0000

3 200.0000 100.0000 40.00000

4 100.0000 25.00000 33.33333