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Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
Week in Review, Review of Exam 1
Exam 1 - Expected knowledge (courtesy of Dr. Janice Epstein):
Chapter 1 - Lines and Linear Models
• Draw an appropriate set of labeled axes for a given problem.
• Graph lines and find intercepts.
• Find the slope of a line given two points on the line.
• Recognize positive, negative, zero and undefined slopes.
• Decide on dependent and independent variables.
• Understand parallel and perpendicular lines.
• Use the point-slope form of a line to find the equation of a line.
• Find the intercepts of a line.
• Use the models for Cost&Revenue&Profit, Supply&Demand, Depreciation
• Find the intersection point for two lines.
• Interpret the Break-Even point or the Equilibrium point.
• Find the vertex and intercepts of a quadratic function
• Find quadratic revenue and profit equations.
• Find maximum profit or revenue with a quadratic model.
Chapter 2 - Linear Systems and Matrices
• Set up a system of linear equations from a word problem
• Understand the relationship between graphs and the number of solutions to a system of linear
equations
• Know the theorem for the number of solutions of a system of linear equations.
• Solve a system of linear equations using Gauss-Jordan elimination method.
• Recognize when an augmented matrix is in row-reduced form.
• Interpret the resulting equations when an augmented matrix is in row-reduced form.
• Represent data in a labeled matrix.
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Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
• Add, transpose and multiply by a scalar.
• Multiply two matrices.
• Interpret the results of matrix multiplication.
Review Problems
Disclaimer: Not every topic is covered in this review. Please also take a look at the previous
Week-in-Reviews for more practice problems.
1. A printer is purchased in 2006 for $25,000. It has been determined that this printer will be
depreciated linearly over a 15 year period. If it is known that the book value of the printer is
$15,000 in 2014, what is the scrap value of this printer?
2. A company making blankets incurs a total cost of $3375 when producing 250 blankets and a
total cost of $3750 when producing 300 blankets. The company sells the blankets for $20 each.
(a) What are the fixed costs for this company?
(b) Find the companys linear profit function.
(c) What is the break-even point for this company?
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Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
3. Danny has to replace a piece of equipment in his shop. He can buy an Alpha machine that
costs $125,820 and takes $83 dollars to maintain each week, or he can buy a Beta machine that
costs $87,500 and takes $163 dollars to maintain each week. How many weeks will it take for
the choice of the Alpha machine to be less expensive than that of the Beta machine?
4. The Andersen’s family has three party celebrations this month. For the first party they need 14
cupcakes, 2 bottles of soda and 13 party favors. For the second party they need 23 cupcakes, 4
bottles of soda and 12 party favors. For the third one they need 24 cupcakes, 5 bottle of soda
and 18 party favors. Each cupcake costs $.45, each bottle of soda $1.39, and each party favor
$5.30. Set up two matrices whose product shows how much the Andersen’s family will spend
for each party as far as cupcakes, soda and party favors.
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Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
5. At a unit price of $5, consumers in College Station will demand 15,000 Maroon Out T-Shirts.
But for each $1 increase in price, they will demand 2,000 fewer T-shirts. The suppliers of the
Maroon Out T-Shirts will not produce any T-shirts if the selling price is $3 or less, but at a
unit price of $8, they are willing to supply 30,000 T-shirts. What is the market equilibrium for
Maroon Out T-shirts?
6. An investor has $50,000 he invests into three accounts yielding 2%, 8%, and 4% interest/year,
respectively. If he earns a total of $4,000 interest in one year, and if he invests twice as much
at 4% as he does at 2%, how much does he invest in each account?
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Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
7. Use the following matrices to determine which of the products below make sense. Bolli Bros.
and Pizza Nut are two restaurants which each sell pizza rolls (in batches of 6 rolls), calzones
and orders of cheese sticks. The prep and cook times for each food item is given, as well as the
number of items two school districts will order.

Pizza Rolls

Calzone
A=

Cheese Sticks
B=
Prep Time (min)
Cook Time (min)
"
Bollis Bros Pizza Nut

$5.95
$8.00
$6.95
$9.99 

$3.95
$6.99
Pizza Rolls Calzone Cheese Sticks #
5
3
2
6
7
6
BISD CSISD

Pizza Rolls
100
85

Calzone
100 
C=
 75

Cheese Sticks
50
60

(a) BA =
(b) AB =
(c) BC =
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Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
8. A gadget manufacturer has cost function given by C(x) = 0.02x2 + 7.5x + 600 dollars for
10 ≤ x ≤ 100, and sells the gadgets for $20 each. Find the revenue function and the breakeven point. Round your your answer to the nearest integer if necessary.
9. Which matrices are in row-reduced form? If not, what operations would make them into
row-reduced form?
#
"
#
"
1 2 0 0 8
1 2 0 0 8
0 0 0 0 1
0 0 0 0 1
10. Solve the systems.
(a) 4x2 − 3x3 − 5x4 = 7
x1 − 2x2 + 3x4 = 8
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Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
(b) x + 2y + 6z = 5
− x + y − 2z = 3
x − 4y − 2z = 1
11. In the matrix equation below find a and b.
"
7 a
2 −4
#T "
1 4 −1
2 5 −3
#
−
h
b 2
iT h
7
8 1 −3
i
"
=3
−29/3
11
2/3
−9
−34/3 7
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Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
12. Jeff operates a mobile car washing business. His fixed monthly costs are $250 and it costs him
$3 to wash a car. When he charged $20 a car, he washed 70 cars a month. He raised the price
to $25 a car and his business dropped to 50 card a month.
(a) What price should he charge to maximize revenue, and what is the maximum revenue?
(b) What price should he charge to maximize profit, and what is the maximum profit?
(c) What are the break-even point(s), and what do they mean?
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