IE 2001: OPERATIONS RESEARCH
(Homework Assignment 3: Due February 06, 2014)
1.
Answer Question 51, p. 122 of the text (Silvco).
2.
A company supplies fertilizers to its customers on a make-to-order basis by
blending appropriate amounts of stock fertilizer
IE 2001: OPERATION RESEARCH
(Homework Assignment 2: Due January 30, 2014)
1) Go over the LP problems we have formulated thus far in class and read Chapter 3 of
the text, which provides numerous other examples of LP formulations. You may skip
Sections 3-2
I.E.2001 OPERATIONS RESEARCH
(Homework Assignment 6: Due Wednesday, Feb. 26, 2014 by 1 PM)
Question 1. Use LINDO or SOLVER or any other software of your choice to find the optimum
solution to Question 51, page 122 (the Silvco transistor refiring problem)
I.E.2001 OPERATIONS RESEARCH
(Homework Assignment 8: Solutions)
Question 1:
Question 1, page 398 of the text (five employees & four jobs.)
After adding a dummy job column and M to denote the cost of disallowed assignments we obtain the
following cost matr
I.E. 2001 OPERATIONS RESEARCH (Spring 2014)
(Solutions to Assignment 3)
Question 1 (Q. 51, p. 122)
Let
X1 = number of transistors worth of germanium melted by method 1
X2 = number of transistors worth of germanium melted by method 2
RD = number of defecti
I.E. 2001 OPERATIONS RESEARCH
(Solutions to Assignment 6)
QUESTION 1
Output is shown below; the variable definitions are as stated in the solutions to
Assignment 3 that were posted earlier.
MIN
50 X1 + 70 X2 + 25 RD + 25 R1 + 25 R2 + 25 R3
SUBJECT TO
2)
0
I.E. 2001 OPERATIONS RESEARCH (Spring 2014)
(Solutions to Assignment 2)
Question 5, p. 114
Define A = Dollars invested in investment A
B = Dollars invested in investment B
C = Dollars invested in investment C
Tj = Dollars invested in T-bills at the end of
I.E. 2001 OPERATIONS RESEARCH
(Solutions to Assignment 9)
Question 1
Define xj = 1 if player j starts; j=1,2,3,4,5,6,7
0 otherwise.
Then the appropriate IP is as follows:
Maximize Z = 3x1 + 2x2 + 2x3 + x4 + 2x5 + 3x6 + x7
st
1. x1 + x2 + x3 + x4 + x5 + x6
I.E.2001 OPERATIONS RESEARCH
(Homework Assignment 7: Due Thursday, Mar. 20, 2014)
Question 1:
Construct the duals for each the following LP problems do not try solving anything!
Minimize
st
Z = 4x1 + 3x2
2x1 + x2 25
-3x1 + 2x2 15
x1 + x2 15
x1, x2 0
Maxim
I.E. 2001 OPERATIONS RESEARCH
(Spring 2014: Solutions to Assignment 4)
Question I
First add nonnegative slacks or subtract nonnegative excess variables (from the first two
constraints) to make all constraints equalities. Then multiply both sides of equati
I.E. 2001 OPERATIONS RESEARCH
(Spring 2014)
(Solutions to Assignment 1)
Question 1
Define R = no. of units of the Orange model to be produced over the next quarter
T = no. of units of the Tangerine model to be produced over the next quarter
Maximize Reven
I.E.2001 OPERATIONS RESEARCH
(Homework Assignment No. 4: Due Feb. 13, 2014)
I.
Restate the following LP so that it is in the standard form - do NOT try solving it.
Max -3X1 + X2 - 2X3 + X4
-4X1 + X2 + X3
> 4
3X1 - X2 + 2X3
< -6
X2 + 4X3 - X4 = -1
st
2X1 -
IE 2001: OPERATION RESEARCH
Homework Assignment 1: (Very!) Simple LP Models
(Due: January 23, 2014)
Please read Chapter 1 and also start to read Chapter 3 (you may skip Sections 3.2 and
3.3 for now). Then answer the following LP modeling questions I only
I.E. 2001 OPERATIONS RESEARCH
(Solutions to Assignment 11)
Question 1.
G, 4
B, 3
E, 5
H, 2
L, 7
START
0
F, 4
A, 4
M, 8
I, 3
K, 5
C, 8
FINISH
0
J, 5
D, 6
By examining all possible paths from the Start to the Finish node, the longest path appears to be
alon
I.E.2001 OPERATIONS RESEARCH
(Homework Assignment 11: Solutions)
Question 1.
Fort Wayne
290
Evansville
217
Gary
113
201
164
Terre Haute
196
58
South Bend
Total length = 58+79+164+113 = 414 miles
Question 2.
1800
Cleveland
Phoenix
900
400
400
900
1100
New
I.E. 2001 OPERATIONS RESEARCH
(Solutions to Assignment 9)
Question 1 (Q20, p. 504-505)
Define AB = 1 if a rep is assigned to states A and B, 0 otherwise;
BC = 1 if a rep is assigned to states B and C, 0 otherwise; etc. etc.
Note that this is a set coverin
I.E. 2001 OPERATIONS RESEARCH
(Homework Assignment 9: SOLUTIONS)
Question 1: (Q4, p.399)
Since Persons 2 and 3 can do two jobs each we make two copies of each of these persons assign
to allow for this possibility. Thus we now have 5 "people" and 4 jobs so
I.E. 2001 OPERATIONS RESEARCH
(Solutions to Assignments 8)
Question 1
Minimize
st
Z = 8x1 - 2x2
9x1
12
2x1 - 7x2 15
-3x1 + x2 21
x1, x2 0
All inequality constraints are normal ( for a Min problem) so we can proceed directly to the dual:
Maximize
st
W = 1
I.E. 2001 OPERATIONS RESEARCH
(Solutions to Assignment 6)
QUESTION 1
Output is shown below; the variable definitions are as stated in the solutions to
Assignment 3 that were posted earlier.
MIN
50 X1 + 70 X2 + 25 RD + 25 R1 + 25 R2 + 25 R3
SUBJECT TO
2)
0
I.E. 2001 OPERATIONS RESEARCH
(Solutions to Assignment 4)
Question I.
First ensure that all constraints are equalities: subtract a nonnegative excess variable X5 from
constraint 2 and add a nonnegative slack variable X6 to constraint 3. Also, rearrange co
I.E. 2001 OPERATIONS RESEARCH (Spring 2013)
(Solutions to Assignment 3)
Question 1 (Q. 51, p. 122)
Let
X1 = number of transistors worth of germanium melted by method 1
X2 = number of transistors worth of germanium melted by method 2
RD = number of defecti
I.E. 2001
OPERATIONS RESEARCH
(Solutions to Assignment 2)
4. SUNCO
Let B = Thousands of barrels of oil purchased each day
HS = Thousands of barrels of heating oil sold directly each day
HP = Thousands of barrels of heating oil processed in the cracker and
I.E. 2001 OPERATIONS RESEARCH
(Spring 2013)
(Solutions to Assignment 1)
Question 1
Define B = no. of barrels of beer produced
A = no. of barrels of ale produced
Maximize Revenue = 5B + 2A
st
5 B + 2A 60
(Limit on corn available)
2 B + A 25
(Limit on hops
I.E. 2001 OPERATIONS RESEARCH
(Solutions to Assignments 7)
Question 1
Z = 4x1 + 3x2
2x1 + x2 25
-3x1 + 2x2 15
x1 + x2 15
x1, x2 0
All inequality constraints are "normal" ( for a Min problem) so we can proceed.
The dual is
1)
Minimize
st
Maximize
st
W = 25