Math 160
Special Assignment #1
Lowman
Spring 2010
•
Due Thursday, Feb 11 in discussion time
•
Calculators can be used to do matrix calculations only where specified. Otherwise, all cal
culations must be done by hand and you must show all work. When using elementary row
operations, you must show your work using the same method that was used in lectures (see
web notes).
1. Use the graphical method to solve the linear programming problem. You must graph the area
of feasible solutions then list all corner points and z values in a table. Show all work.
Maximize
z
= 6
x
+ 5
y
Subject to
3
x
+ 2
y
≤
120
4
x
+ 6
y
≤
260
x, y
≥
0
2. Use the graphical method to solve the linear programming problem. A truck traveling from
New York to Baltimore is to be loaded with two types of cargo. Each crate of cargo A is
8
cubic feet in volume, weighs
100
pounds, and earns
$10
for the driver. Each crate of cargo
B is
4
cubic feet in volume, weighs
200
pounds, and earns
$12
for the driver. The truck can
carry no more than
400
cubic feet of crates and no more than
10
,
000
pounds.
Also, the
number of crates of cargo A must be less than or equal to twice the number of crates of cargo
B. Maximize drivers earnings subject to constraints.
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 Spring '08
 DOYLE
 Math, Linear Algebra, Gaussian Elimination, GaussJordan elimination method

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