{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# hw11s - ENGRI 1101 Engineering Applications of OR Fall 08...

This preview shows pages 1–2. Sign up to view the full content.

ENGRI 1101 Engineering Applications of OR Fall ’08 Homework 11 Homework 11 Solutions 1. Let’s number the empty squares in the grid as follows: The ﬁrst instinct in formulating this problem as an IP is to deﬁne 10 variables to represent the values assigned to each of the 10 empty squares on the grid. However, we will then have to impose constraints that say that the assigned values are all diﬀerent — not something that can be done with linear constraints on variables at hand! So, instead, we will deﬁne the following decision variables: x ij = ± 1 if number i is assigned to square j, 0 otherwise , for i = 0 , 1 , . . . , 9 and j = 1 , . . . , 10. We need constraints so that each number is assigned exactly to one square: 10 X j =1 x ij = 1 for each i = 0 , 1 , . . . , 9 , and each square must get exactly one number: 9 X i =0 x ij = 1 for each j = 1 , . . . , 10 . Now, we also need constraints that ensure that the numbers in each row and column add up to 22. To do that, we need to be able to evaluate the actual number assigned to a particular square of the grid. Consider square

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

hw11s - ENGRI 1101 Engineering Applications of OR Fall 08...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online