ISyE 3133B Sample Test 3
Time: 50 minutes, 50 Points
Set A
Problem 1 (15 pts).
The partial sensitivity report below corresponds to an optimal solution to a minimization LP with 3 nonnegative variables (x1 , x2 , x3 ) and 3 constraints. The constraints are
ISyE3133B Sample Test II
Time Limit: 50 min
(LP: modeling + concepts + simplex method + duality)
Set A:
1.
[10 points] Consider an LP of the form
max
1
1, . . ,
0
s. t.
1, ,
where all problem parameters are positive integers.
a) Argue that the above LP al
ISyE 3133B Sample Final Tests
Time: 160 minutes, 100 Points
Set A
Problem 1 (20 pts).
Head & Boulders (H&B) produces two dierent types of shampoos A and B by mixing 3 raw materials (R1,
R2, and R3). The amount of each raw material per pound of each shampo
HW 7 Solution (ISYE 3133B)
1. #10. We need x + y-30 or 2x + 5y-120 or both. From the book,
(26)' and (27)' we see that we must add the constraints
x + y-3Mz
2x + 5y-12M(1-z)
z = 0 or 1 , M a large number
#11. We have that x<3 (or 3-x>0) implies y3 (or 3-y
HW 6 Solution (ISYE 3133B)
Problem Set I:
Question 1:
(a). If the engineer can get us 200 extra gallons of A per day, the rhs of constraint 1
decreases by 200 which is in the allowable range. So the decrease in the objective value
= 13.3333 * 200 = 26662/
Solutions
ISYE 3133b (Dr. Ahmed): Homework 5
Problem 1
INDICES
t cfw_1, 2, . . . , 5
DATA
rt = Number of drivers required in year t.
DECISION VARIABLES
ht = Number of drivers hired at beginning of year t.
ft = Number of drivers red at beginning of year t.
Solutions
ISYE 3133b (Dr. Ahmed): Homework 4
Problem 1
(a) See the LP below:
20
max
xi
i=10
95
95
xi
s.t. 26
i=0
95
ixi 34
i=0
xi (avg. between 26 and 34)
i=0
95
xi = 650, 500 (total population)
i=0
49
95
xi 2
i=0
xi (number under 49 is greater than twic
Solutions
ISYE 3133b (Dr. Ahmed): Homework 3
Problem 1
Let
st = shirts produced in month t regular time.
st = shirts produced in month t, overtime.
pt = pants produced in month t, regular time.
pt = pants produced in month t, overtime.
it = shirt inventor
Solutions
ISYE 3133b (Dr. Ahmed): Homework 2
Problem 1
(a) Amount deposited must be no less than the amount of money withdrawn during each of May-July.
y t zt
t cfw_5, 6, 7
(b) Total amount deposited must be no less than total amount of money withdrawn.