Assigned: January 25, 2013
Due: February 1, 2013
MATH 326: Homework 2
SPRING 2013
1. A small organic farmer is going to plant soy beans and broccoli. Assume that each
acre of soybeans earns $100 and each acre of broccoli earns $175. Each acre of soy
beans
Assigned: April 19, 2013
Due: April 26, 2013
MATH 326: Homework 10
SPRING 2013
1. Suppose that I wish to start a new diet consisting of Raman noodles, ice cream (from
Ferdinands) and salad (from the Broiler). Each serving of Raman noodles costs $1.
Each s
Assigned: March 30, 2013
Due: April 5, 2013
MATH 326: Homework 8
SPRING 2013
1. Consider the linear programming minimization problem
min
cT x
s.t. Ax b
x0
Under what conditions should a non-basic variable enter the basis? State and prove
an analogous theo
Assigned: April 8, 2013
Due: April 15, 2013
MATH 326: Homework 9
SPRING 2013
1. Suppose I provide
z
z 1
x1 0
x2
0
you with the following Tableau:
x1 x2 s 1
s2 RHS
0
0
a
b
2
2
1
1
0 3 3
1
0
1
1
3
2
3
1
(a) If I tell you this is an optimal tableau for a min
Assigned: March 18, 2013
Due: March 22, 2013
MATH 326: Homework 7
SPRING 2013
1. A pet day spa specializes in pampering cats and dogs. Each cat brings in $40 in
revenue, while each dog brings in $60 in revenue. Dogs and cats both require 1 hour
to bathe a
Assigned: February 24, 2013
Due: March 1, 2013
MATH 326: Homework 6
SPRING 2013
1. Consider the polyhedral set P from HW # 5 (Problem 3) dened by the linear
inequalities:
3x1 + x2 11
x1 + x2 5
x1 3
x1 0
x2 0
(a) Compute the equations and inequalities deni
Assigned: February 3, 2013
Due: February 8, 2013
MATH 326: Homework 3
SPRING 2013
1. Show that the vectors
1
4
x1 = 2 , x2 = 5 ,
3
6
7
x3 = 8
9
are linearly dependent. [Hint: Following the example shown in class, create a matrix
whose columns are the
Assigned: January 16, 2013
Due: January 25, 2013
MATH 326: Homework 1
SPRING 2013
1. Solve the following problem using elementary calculus techniques.
min (x 5)2 + (y 5)2
subject to
x+y =5
[Hint: We did this in class with the goat problem. Solve for y and
Assigned: February 4, 2013
Due: February 15, 2013
MATH 326: Homework 4
SPRING 2013
1. Show that the vectors
x1 =
1
1
,
2
1
x2 =
form a basis for R21 . [Hint: (i) Show that the vectors are linearly independent. (ii)
Show that you can nd coecients 1 and 2 s
Assigned: February 5, 2013
Due: February 22, 2013
MATH 326: Homework 5
SPRING 2013
1. Prove that every polyhedral set is convex.
2. Prove the following: Let C Rn be a convex cone and let x1 , x2 C. If , R
and , 0, then x1 + x2 C. [Hint: Use the denition o