67.411/92.473 OR I, Homework 3 AMPL Models.

Oil refinery model (E&K, section 2.2)

Model file

set GASOLINE;
set PROCESS;
set GRADES;

param profit {GASOLINE} >= 0;   # profit on sale of an item of a product

param crude_used {PROCESS, GRADES} >= 0; # amount of crude used
                                           # in a particular process

param gas_produced {PROCESS,GASOLINE} > 0;  # amount of gasoline produced
                                            # in a particular process

param crude {GRADES}; # limit on amount of crude available

param require {GASOLINE} >= 0;
        # amount of gasoline required

var runs {i in PROCESS} >= 0; # number of runs of a process

maximize total_profit :
   sum{i in GASOLINE} profit[i]*(sum{j in PROCESS} runs[j]*gas_produced[j,i]);
           #  profit from selling gasoline

subject to min_requirements {i in GASOLINE}:
   sum{j in PROCESS} runs[j]*gas_produced[j,i] >= require[i];

subject to crude_available {j in GRADES}:
   sum{i in PROCESS} runs[i]*crude_used[i,j]  <= crude[j];

Data file:

set GASOLINE := regular super;
set PROCESS := older newer;
set GRADES := A B C;

param:     profit  require :=
  regular     6      500
  super       9      300;

param crude_used :
           A   B   C  :=
  older    5   7   2
  newer    3   9   4;

param crude  :=
  A  1500
  B  1900
  C  1000;

param gas_produced :
        regular  super  :=
   older   9      7
   newer   5      9  ;

Solution:

MINOS 5.4: optimal solution found.
1 iterations, objective 31757.14286
runs [*] :=
newer    0
older  271.429

Electric power model (E&K, Question 2.15)

var  a >= 0;
var  b >= 0;
var  c >= 0;

maximize steam: 22000 * a + 26000 * b + 32000 * c;

subject to capacity: a + b + c <=25;
subject to particulates: a + 3 * b + 2 * c <= 15;
subject to sulfur: -1300 * a + 1200 * c <= 0;

Solution:

MINOS 5.4: optimal solution found.
1 iterations, objective 680000
a = 15
b = 0
c = 0

Advertising model (AMPL book, question 1.1)

var  tv >= 10;
var  magazines >= 2;
var  radio >= 0, <= 120;

maximize audience: 1.8 * tv + magazines + .25 * radio;

subject to budget: 20000 * tv + 10000 * magazines + 2000 * radio <= 1000000;
subject to create: tv + 3 * magazines + (1/7) * radio <=100;

Solution:

(a):
MINOS 5.4: optimal solution found.
1 iterations, objective 98
tv = 10
magazines = 80
(b):
MINOS 5.4: optimal solution found.
2 iterations, objective 92
tv = 40
magazines = 20
(c):
MINOS 5.4: optimal solution found.
1 iterations, objective 118
tv = 10
magazines = 0
radio = 400
(d):
magazines >= 2:
MINOS 5.4: optimal solution found.
1 iterations, objective 117.5
tv = 10
magazines = 2
radio = 390

radio <=120:
MINOS 5.4: optimal solution found.
3 iterations, objective 100.1942857
tv = 29.0286
magazines = 17.9429
radio = 120