c
Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
Week in Review, Sections 1.Q, 2.1-2
1. Consider the following two quadratic equations.
(a) Determine whether the graph opens up or down.
(b) Find the vertex of the parabola.
(c) Find the maximum and minimum values.
(d) Find the x-intercepts
(i) y = 25x2 − 10x + 1
(ii) y = −7(x + 4)2 + 10
c
Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
2. The price-demand equation of an item is given by p(x) = 150 − x (where x is the number of
items). The fixed costs of production are $500, and the cost of producing each item is $90.
(a) Find the revenue function.
(b) Selling how many items maximizes the revenue?
(c) Find the break-even point(s).
(d) Selling how many items maximizes the profit, and what is the maximum profit?
c
Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
3. Solve the following systems of equations.
(a) 3x − y = 7
6x + 2y = 10
(b) 4x − 2y = 6
8x − 4y = 16
(c) For what value(s) of k will the system of equations has exactly one solution?
−2x + 3y = 9
kx − 2y = −6
c
Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
4. State whether the following matrices are in row-reduced form. If the matrix is NOT in rowreduced form, what would be the next row operation needed in the Gauss-Jordan Elimination
Method?


1 0 0 2


(a)  0 1 0 3 
0 1 2 4
"
1 2 0 3
0 0 1 4
"
1 2 3
0 1 −2
(b)
(c)
#
#


1 0 0 2

(d) 
 0 1 3 −4 
0 0 0 0
5. Pivot the following matrix about the boxed element. Indicate the row operations used.
1 2
4 −3


 0 3 −9 12 
0 −5 2
1


c
Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
6. Solve the system of equations using the Gauss-Jordan elimination method by demonstrating
all required row operations.
−3x + y + 2z = 8
8x + 3y − 2z = 9
x − 2y + 2z = 3
c
Math 141, Fall 2014, Dr.
Kamran Reihani - Texas A&M University
7. An airline is considering the purchase of seven aircraft to meet an estimated demand for 1800
seats. They have $760 million to spend on three types of planes: Boeing 747s, Boeing 777s, and
Airbus A321s. The table below shows number of seats and costs (in millions) of each plane.
How many of each plane should the airline order to meet its demand for seats?
Aircraft
Boeing 747
Boeing 777
Airbus A321
Seats Cost
400
200
300
160
200
60