#4

STORM

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!