Chapter 2An Introduction to Linear Programming
MULTIPLE CHOICE
1. The maximization or minimization of a quantity is the
a. goal of management science.
b. decision for decision analysis.
c. constraint
EX 4: MATHEMATICAL MODELLING: Linear Regression (on Cale):
The following table gives the data of retail sales of prescription drugs for certain years. Model the data
with a linear function, using line
1.6 LINEAR INEQUALITIES > 4 > 4
EXAMPLES: Show the solution on a number line.
Jé («a 1]
1. 12~8y_>.10y~6
w/Kj 3, r}?
J 5 /
. 0 J
2. 2x4(3+2x)<3-(4x2)
Qx/gwg-y43Ax 42. :7
7C é '1) «6)
Walk < /? -
.
MATH 140 1.1 Introduction to Graphing
A: LINEAR FUNCTIONS:
and
EX: 3): + 2y = 6 a) Graph >
X
0 5 (5-;mme)
L O . b) IS pt. (1;4) on the line?
(x.Maur*)cl.got_ 30,) +2) I No
@ 5 351, J
c) Pt. (1;k) is o
1.5 SOLVING LINEAR EQUATIONS and 1.6 LINEAR INEQUALITIES
Solve the following equations:
1. 2(2x3)=(x6)
07. 21143 T ,7: +
X : 1
X T v/
:0 \0 0
2 _13
2 3*;3630'
gowi : l3
j «I?
~ I7
9. 4
x + 1(Qwrs) :
GRAPHING CALCULATOR
To graph a function:
0 Enter mction y z
0 Set Window :
0 Trace > use to locate a point if x- coordinate is given
0 Xintercept(s)/ Zeros: y2 = 0 enter and use
intersection key
o I
1.2 FUNCTIONS AND GRAPHS
FUNCTIONS
H: I) A chircalgc rchhauskc'fg MM 'a 74:7,3V7
IIW Vd/ux/ (K 3 John}. )3 @2139 Malt 014 (011/7 0W6)
We Value, Cy) . rave)
Functions can be expressed as:
L awn/) Jive-
CHECK UP:
1. Find the length of AB, with A (8, -5) and B{-2, 4) . Express answer to two decimal places.
5145 90674. (AW .- g/ m i ; v.82
2? 25
2. Find the equation of the circle in which a diamet
TWO MORE FORMULAS
The General Form of the linear function:
PRACTICE:
Rewrite the following functions in general form:
y=-:-x+4
3g; 3:] : 2x+|z
QXIBJ : ~41
6?"
"
vaad +\2 r 0
TWO SPECIAL CASES:
b co
Owgcg lob-I)+(§~DT& -MOLLL .
: S3 l v
4. Find the Equation of the circle with CENTRE: (~6;5) , and the circle passes through the point: (1;7) .
l 1 g z
Lx¢®>+(jvsy:g3_' (ad:
5. Given the points: A( -