IENG 553
Homework # 2b with Solutions
(Continue Review of Linear Algebra)
Problem:
Find the extreme direction(s) for each of the following convex sets.
a) X = cfw_(x1, x2): 3x1 + 4x2 > 12, 2x1 + x2 > 6, x1 > 0, x2 > 0
b) X = cfw_(x1, x2): 3x1 + 4x2 > 12,

IENG 553
Homework # 2a Solutions
(Review of Linear Algebra)
I. Textbook Problems
Problem 2.1
The vectors are linearly independent and k = n. Still linearly independent with the new a2, so still a basis.
Problem 2.2
a) Spanning set, basis
c) Spanning set,

IENG 553
Homework # 1a Solutions
I. LP Models/Formulation
Problem 1.2: Has 6 constraints & 4 variables. Also, x4 = 1, which means 1 kg of chemical compound 4 is
used to form one kg of the product and z* = 15, which means the cost per kg of the product is