College Algebra 9th txtbk

SECTION 7–2 Solving Systems of Linear Equations Using Gauss–Jordan Elimination 441
tively. How many of each type of product should be manufactured
each week in order to exactly use the weekly allocations?
Product Desk Chair File Cabinet Printer Stand
Labor $30 $35 $40
Materials $45 $60 $55
Shipping $25 $20 $15
69. PRODUCTION SCHEDULING A company has plants located in
Michigan, New York, and Ohio where it manufactures laptop computers,
desktop computers, and servers. The number of units of
each product that can be produced per day at each plant are given
in the table below. The company has orders for 2,150 laptop computers,
2,300 desktop computers, and 2,500 servers. How many
days should the company operate each plant in order to exactly fill
these orders?
Plant Michigan New York Ohio
Laptop 10 70 60
Desktop 20 50 80
Server 40 30 90
70. PRODUCTION SCHEDULING A company has plants located in
Maine, Utah, and Oregon where it manufactures stoves, refrigerators,
and dishwashers. The number of units of each product that can be produced
per day at each plant are given in the table. The company has
orders for 1,500 stoves, 2,350 refrigerators, and 2,400 dishwashers.
How many days should the company operate each plant in order to
exactly fill these orders? Set up a system of equations whose solution
would answer this question and solve the system.
Plant Stoves Refrigerators Dishwashers
Maine 30 70 60
Utah 20 50 50
Oregon 40 30 40
71. INVESTMENT Due to recent volatility in the stock market,
Catalina’s financial advisor suggests that she reallocate $70,000 of
her retirement fund to bonds. He recommends a mix of treasury
bonds earning 4% annually, municipal bonds earning 3.5% annually,
and corporate bonds earning 4.5% annually. For tax reasons,
he also recommends that the amount invested in treasury bonds
should be equal to the sum of the amount invested in the other categories.
If Catalina follows these recommendations, and the goal is
to produce $2,900 in annual interest income, how much will she invest
in each of the three types of bonds?
72. INVESTMENT When the real estate market begins to rebound,
Catalina (see Problem 71) decides to reallocate her investment mix.
At this point, her investment has grown to $76,000. She’ll leave
some money in treasury and corporate bonds, but will replace municipal
bonds with a real estate investment trust that guarantees a
6.5% annual return. If she plans to leave as much in treasury bonds
as the sum of the other two investments, how much should she
invest in each to reach her new goal of earning an annual interest
income of $3,600?
7-2
Solving Systems of Linear Equations Using
Gauss–Jordan Elimination
Z Matrices and Row Operations
Z Reduced Matrices
Z Solving Systems by Gauss–Jordan Elimination
Z Application
In this section, we introduce Gauss–Jordan elimination, a step-by-step procedure for solving
systems of linear equations. This procedure works for any system of linear equations
and is easily implemented on a computer. In fact, the TI-84 has a built-in procedure for performing
Gauss–Jordan elimination.
Z Matrices and Row Operations
In solving systems of equations using elimination by addition, the coefficients of the variables
and the constant terms played a central role. The process can be made more efficient