These problems are a sample of the kinds of problems
that may appear on the final
exam. Some answers are included to indicate what is expected. Problems that
require
a summary statement are marked with Sum . The summary statements should be
written in complete sentences and they should include the units of measurement
for
all quantities mentioned in the summary .
1. (Worked Example: READ IT!) Both of the Mathematics Departments at CSU
Northridge
and Fullerton give final exams in College Algebra (CA) and the Mathematical
Methods for
Business (BM). This uses resources from the department faculty (F) to make the
exams, the
staff (S) to copy the exams and the teaching assistants (T) to proctor the
exams. Here are
the labor-hour and wage requirements for administering each exam:
| |
Faculty |
Staff |
Teaching Assistants |
| Business Math Exam |
5.0 hrs work |
0.5 hrs work |
2.0 hrs work |
| College Algebra Exam |
7.0 hrs work |
1.0 hrs work |
2.0 hrs work |
| |
CSUN |
CSU, Fullerton |
| Faculty |
$40 per hour |
$50 per hour |
| Staff |
$14 per hour |
$16 per hour |
| Teaching Assistants |
$8 per hour |
$10 per hour |
The labor-hours and wage information is given in the
following matrices:
(a) Compute the product MN
Answer:
(b) What is the (1, 2)-entry (also known as R1C2) of
matrix MN and what does it mean?
Summary : The (1, 2)-entry of MN is 278.
$278 are spent on labor to make up the Business
Math Exam at CSU Fullerton. |
2. Delta Duplex Properties builds two-family dwellings.
They have two models : Economy Model,
Deluxe Model. The cost to build depends on the square footage of the building
and the size
of the lot. Of course, the Deluxe Model building and lot are larger than the
Economy Model.
Square footage and costs per square foot are given in the tables below:
| |
Size of building |
Size of lot |
Economy Model
Deluxe Model |
2300
3000 |
7000
9000 |
Sizes are given in square feet .
| Building cost |
Lot cost |
| $300 |
$100 |
Costs are given in dollars per square foot .
The size and cost information is given in the following matrices:
(a) Compute the product SC .
(b) Sum Explain what each of the entries in the product SC means.
