#4
Exercise
The
problem:
Zmax =
5X1
+ 3X2 + 4X3
subject
to:
b1: X1 + 3X3 <=
30
b2: 2X2 + X3 >=
15
b3: 3X1 + 2X2 <= 10
Choose:
1) Linear & Integer
Programming
Choose:
2) Create a new data
set
Type
in:
Title: STORM
Exercise 1 your
name
Number
of variables:
3
Number
of constraints:
3
Starting
solution given:
no
Objective
type (MAX/MIN):
MA
Ready
to go on to detailed data?
Enter:
y
Change:
Three
column labels: VAR 1, 2, 3 to
X1, X2, X3
Change:
Three
row labels: CONSTR 1, 2, 3 to
b1, b2, b3
Enter:
the
following in the OBJ COEFF row:
X1: 5
X2: 3
X3: 4
(See
the objective function above in order to understand these
values.)
Enter:
the
values in the b1 row:
b1: X1:
1 X2: 0
X3: 3 RHS:
30
(See
the constraints above in order to understand these
values.)
Enter
the values in the other two rows:
b2:
b3:
VARBL
TYPE
This
is nonnegativity. Keep as POS (the
default value).
Hit:
<F7> Done
Choose:
4) Execute the
module
Choose:
1) Go to the optimal
solution
Choose:
2) Detailed report
Questions:
a) What are the BASIC variables in the
optimal
solution?
b) What are the values of each of these
variables?
c) What is the
profit?
d) So what is the optimal solution … in
plain
English?
Hit:
<Print
Screen>
Hit:
<Enter> to get to next
screen
Hit:
<Print
Screen>
Another
question:
e) What does “shadow price”
mean?
Hint: Go back to the data entry screen and change the value of b1 from 30 to 31. Execute the model.
Go to the optimal
solution.
Detailed report.
What
has changed? Why? This should help explain what a “shadow
price” is.
Save
the file:
Get
to the original screen and Choose:
2) Save the current data set on your
disk.
Type
in a filename
NOW
TRY …
Enter
the values from assignment #2 (handout #3) – then you’ll have your answers
for
this homework assignment!