The constraints will change to:
j
8
j =1 xj
xj uj
25
(0.1)
To express the objective
min cfw_ max rj xj min rj xj
j
j
we wil need two new variables; z1 , a lower bound on the rj xj s, and z2 , an upper bound.
So the complete formulation will be
min z2 z

NOTE: There are 2 correct solutions to both problems. One is more compact,
the other is more clear, but using more variables. In general, if you are not sure
how to formulate a problem, do not shy away from using more variables!
1. Modify the parfume prod

STOR 612 Final exam, Fall 2011
The exam is three (3) hours, closed book, closed notes, no calculators.
Problem 1 (20 points)
We are given a knapsack with capacity n, and items 1, . . . , n (i.e. the number of
items is the same as the capacity of the knaps

Final exam
OR 612
Please only use the paper given by the instructor.
Please write your solutions clearly, and legibly. Explain everything you do.
Question 1 (20 points) You are visiting a magical forest in which every inhabitant is
either a knight or a kn

Exam 2
STOR 612
Question 1 (40 points)
Howie Cramms needs to take n nal exams. If he studies h hours on Course #j ,
h = 1, . . . , H , he can obtain p(h, j ) grade points for that course. Suppose he is willing
to study H hours overall, and he wants to kno

STOR 612 Exam 2, 2011
The exam is two hours, closed book, closed notes, no calculators. Problem 2 depends
on the solution of Problem 1.
Problem 1 (20 points)
We are given a knapsack with capacity n, and items 1, . . . , n (i.e. the number of
items is the

Exam 2
STOR 612
Please only use the paper given by the instructor. If a question says PhD next
to it, then it is mandatory ONLY for PhD students. MS students can do the PhD
problems for 50 % of the points, to receive extra credit. (In other words, doing t

STOR 612 Exam 1, 2011
The exam is two hours, closed book, closed notes, no calculators. It has 3 problems. You do not need to give formal proofs of correctness in the LPs in disguise
type problems.
Problem 1 (30 points)
A government agency in North Caroli

First solution
We assume that we are at the rst variant, i.e. employees overwork on their day
after their 5 day shift.
Variables:
xi : number of employees who start work on day i, and work exactly 5
consecutive days.
yi : number of employees who start