FM Dept Final Exam Review Sp06
Finite MathematicsDepartmental Review Sheet
Spring 2006
(Finite Mathematics, an Applied Approach, 3
rd
Edition
.
Young, Lee, Long and Graening.
Pearson, Addison Wesley,
2004.)
Unless otherwise stated, all work should be done algebraically, all work should be shown, and exact
answers should be given.
Only departmental formula sheets will be allowed for use during the final exam.
[Objective 1, Section 4.3]
1.
Graphically solve the following:
Maximize
y
6x
f
+
=
, subject to:
≥
≤
+

≤
+
0
y
0
y
3x
8
y
x
2.
First formulate the linear program, and then solve it by the graphical method.
Nutrition:
A dietitian is to prepare two foods to meet certain requirements.
Each pound of Food I
contains 100 units of vitamin C, 40 units of vitamin D, and 10 units of vitamin E and costs 20
cents.
Each pound of Food II contains 10 units of vitamin C, 80 units of vitamin D, and 5 units of
vitamin E and costs 15 cents.
The mixture of the two foods is to contain at least 260 units of vitamin
C, at least 320 units of vitamin D, and at least 50 units of vitamin E.
How many pounds of each type
of food should be used to minimize the cost?
[Objective 1, Section 5.2]
3.
Use the simplex algorithm to solve the given linear programming problems.
a.
Maximize
y
2x
f
+
=
Subject to:
0
y
0,
x
20
2y
3x
16
2y
x
20
y
4x
≥
≥
≤
+
≤
+
≤
+
b.
Maximize
3z
3y
2x
f
+
+
=
Subject to:
0
z
0,
y
0,
x
12
z
y
x
10
3z
y
8
2z
x
≥
≥
≥
≤

+

≤
+

≤
+
c.
Advertising:
An advertising agency has developed radio newspaper, and television ads for a
particular business.
Each radio ad costs $200, each newspaper ad costs $100, and each television
ad costs $500 to run.
The business does not want the television ad to run more than 20 times, and
the sum of the numbers of times the radio and newspaper ads can be run is to be no more than 110.
The agency estimates that each airing of the radio ad will reach 1000 people, each printing of the
newspaper ad will reach 800 people, and each airing of the television ad will reach 1500 people.
If
the total amount to be spent on ads is not to exceed $15,000, how many times should each type of ad
be run so that the total number of people reached is a maximum?
[Objective 2, Section 5.3]
4.
Use Crown’s pivoting rules and the simplex method to solve:
a.
Use Crown’s method to maximize
2y
4x
f
+
=
Subject to:
0
y
0,
x
12
y
3x
5
y
x
≥
≥
≤
+
≥
+
1