Deck 4: Graphing and Optimization

Question 1

Solve the problem.
Suppose that the supply and demand equations for a logo sweat shirt in a particular week are eek are for fo
the demand equation; and d , for the supply equation. Find the equilibrium price and quantit for the supply equation. Find the equilibrium price and quantiy.

Answer 1

Equilibrium price: : $ 45; Equilibrium quantity: 100

Question 2

Solve the problem.
Daisy has a desk full of quarters and nickels. If she has a total of 23 coins with a total face value of $4.35, how many of the coins are nickels?

A) 9 nickels
B) 21 nickels
C) 7 nickels
D) 16 nickels

Answer 2

7 nickels

Question 3

Solve the system of equations by graphing.

A) (6, -1)
B) (-1, 6)
C) (1, -6)
D) no solution

Answer 3

(-1, 6)

Question 4

Write the word or phrase that best completes each statement or answers the question.

Question 5

Solve the system of equations by substitution.

A) (-2, 3)
B) (3, 2)
C) (2, 3)
D) (-10, 3)

Question 6

Write the word or phrase that best completes each statement or answers the question.

A) (4, 1)
B) (4, -1)
C) (-4, -1)
D) (-4, 1)

Question 7

Write the word or phrase that best completes each statement or answers the question.

A) (7, 0 )
B) (1 , - 7)
C) (0, - 7)
D) (1, - 8)

Question 8

Solve the problem.
Sam and Chad are ticket-sellers at their class play. Sam is selling student tickets for $2.00 each, and Chad selling adult tickets for $5.50 each. If their total income for 24 tickets was $83.00, how many tickets did Sam sell?

A) 16 tickets
B) 15 tickets
C) 10 tickets
D) 14 tickets

Question 9

Provide an appropriate response.
Given the matrix B: What is the size of B?

A)
B) 3
C)
D)

Question 10

Provide an appropriate response.
Write the augmented matrix for the system.

A)
B)
C)
D)

Question 11

Write the word or phrase that best completes each statement or answers the question.

A) (0, 8)
B) (-8, 0)
C) (0, -8)
D) (8, 0)

Question 12

Write the word or phrase that best completes each statement or answers the question.

A) (3, 9)
B) (9, 3)
C) infinitely many solutions
D) no solution

Question 13

Solve the system of equations by graphing.
Use a graphing utility to solve the system . Give the . Give theanswer to three decimal places.

Question 14

Solve the system of equations by graphing.

A) (3, 2)
B) (-2, -3)
C) (2, 3)
D) no solution

Question 15

Solve the system of equations by graphing.

A) (-2, -1)
B) (-1, -2)
C) (2, 1)
D) no solution

Question 16

Solve the system mentally, without the use of a calculator or pencil-and-paper calculation. Try to visualize the graphs of
both lines.

A)
B)
C)
D)

Question 17

Provide an appropriate response.
Given matrix A: What is the size of A?

A)
B) 3
C)
D)

Question 18

Solve the problem.
A company that manufactures laser printers for computers has monthly fixed costs of sts of $177,000 and variable
costs of f $650 per unit produced. The company sells the printers for s for $1,250 per uni per unt. How many printers must be
sold each month for the company to break even?

Question 19

Solve the system of equations by substitution.

A) (1, 2)
B) (-3, 0)
C) (0, 3)
D) no solution

Question 20

Solve the system mentally, without the use of a calculator or pencil-and-paper calculation. Try to visualize the graphs of
both lines.

A) x = -5; y = 8
B) x = 3, y = 7
C) x = 5; y = -8
D)

Question 21

Provide an appropriate response.
Solve the linear system corresponding to the following augmented matrix:

A) (-2, -5)
B) (5, -2)
C) (-2, 5)
D) (0, 0)

Question 22

State whether the matrix is in reduced form or not in reduced form.

A) Not Reduced Form
B) Reduced Form

Question 23

Provide an appropriate response.
Only one of the following augmented matrices of a linear system is in a reduced form. Choose the matrix that is in reduced form.

A)
B)
C)
D)

Question 24

Identify the row operation that produces the resulting matrix.

A) -R2 + R1 R2
B) R1 + R2 R2
C) R1 + R2 R1
D) -R1 + R2 R2

Question 25

State whether the matrix is in reduced form or not in reduced form.

A) Reduced Form
B) Not Reduced Form

Question 26

Write a system of equations associated with the augmented matrix. Do not try to solve.

A)
B)
C)
D)

Question 27

Provide an appropriate response.
Solve the linear system corresponding to the following augmented matrix:

Question 28

Provide an appropriate response.
Given matrix A:
A = What is the size of A? Find A? Find a and d

Question 29

State whether the matrix is in reduced form or not in reduced form.

A) Not Reduced Form
B) Reduced Form

Question 30

Identify the row operation that produces the resulting matrix.

A) 1
B) 1
C)
D)

Question 31

Perform the indicated row operations on the following matrix.

A)
B)
C)
D)

Question 32

The matrix is the final matrix form for a system of two linear equations in variables x1 and x2. Write the Solution of the
system.

A)
B) No solution
C)
D)

Question 33

Perform the indicated row operations on the following matrix.

A)
B)
C)
D)

Question 34

Provide an appropriate response.
Use the augmented matrix to solve the system:

A) (-0.1, -0.5)
B) (0, 0)
C) (-1, -5)
D) (-5, -1)

Question 35

Identify the row operation that produces the resulting matrix.

A)
B)
C)
D)

Question 36

The matrix is the final matrix form for a system of two linear equations in variables x1 and x2. Write the Solution of the
system.

A)
B)
C)
D)

Question 37

Provide an appropriate response.
Use a graphing utility and augmented matrix methods to solve the system: Express your answer accurate to three decimal places.

Question 38

Provide an appropriate response.
Solve the linear system corresponding to the following augmented matrix:

Question 39

Identify the row operation that produces the resulting matrix.

A)
B) R1 + R2 R2
C)
D)

Question 40

Provide an appropriate response.
Write the augmented matrix for the system.

A)
B)
C)
D)

Question 41

Solve the problem.
A chemistry department wants to make 3 liters of a 17.5% basic solution by mixing a 20% solution with a 15% solution. How many liters of each type of basic solution should be used to produce the 17.5% solution?

A) 1 liter of 15% solution, 2 liters of 20% solution
B) 1.5 liters of 15% solution, 1.5 liters of 20% solution
C) 2 liters of 15% solution, 1 liter of 20% solution
D) 0.5 liter of 15% solution, 2.5 liters of 20% solution

Question 42

Write the linear system corresponding to the reduced augmented matrix.

A) x1 = 4, x2 = t for any real number t
B) x1 = 4, x2 = 0
C) No Solution
D) x1 = -4, x2 = 0

Question 43

Solve using Gauss-Jordan elimination.

A) (-6, 9, 12)
B) (6, 4, 9)
C) (6, 9, 4)
D) No solution

Question 44

Find the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM.
Hurst's Feed & Seed sold to one customer 5 bushels of wheat, 2 of corn, and 3 of rye, for $31.00. To another customer he sold 2 bushels of wheat, 3 of corn, and 5 of rye, for $27.60. To a third customer he sold 3 bushels of wheat, 5 of corn, and
2 of rye for $32.70. What was the price per bushel for each of the different grains?
Let x represent the price per bushel for wheat, y the price per bushel for corn, and z the price per bushel for rye.

A)
B)
C)
D)

Question 45

Find the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM.
There were 35,000 people at a ball game in Atlanta. The day's receipts were $290,000. How many people paid $14 for reserved seats and how many paid $6 for general admission? Let x represent the number of reserved
Seats and y represent the number of general admission seats.

A)
B)
C)
D)

Question 46

Solve using Gauss-Jordan elimination.
4 4

A) (3, -3)
B) (-3, -3)
C) (-3, 3)
D) No solution

Question 47

Find the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM.
In producing three types of bricks: face bricks, common bricks, and refractory bricks, a factory incurs labor,
material, and utility costs. To produce one pallet of face bricks, the labor, material, and utility costs are $50, $75,
and $35, respectively. To produce one pallet of common bricks, the labor, material, and utility costs are $50, $60,
and $30, respectively, while the corresponding costs for refractory bricks are $75, $100, and $45. In a certain
month the company has allocated $12,000 for labor costs, $14,500 for material costs and $6,000 for utility costs.
How many pallets of each type of brick should be produced in that month to exactly utilize these allocations?
Set up a system of linear equations, letting x, y, and z be the number of pallets of face, common, and refractory
bricks, respectively, that must be produced in that month.

Question 48

Solve using Gauss-Jordan elimination.

A) (-5, -6)
B) (-6, -5)
C) (6, -6)
D) (5, -5)

Question 49

Find the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM.
A A $ 000 tru trst is to be invested in bonds paying 9%, CDs paying 8%, and mortgages paying 10%. The sum of the amount invested in bonds and the amount invested in CDs must equal the mortgage investment. To earn an $11,400
Annual income from the investments, how much should the bank invest in each?
Let x represent the amount invested in bonds, y the amount invested in CDs, and z the amount invested in mortgages.

A)
B)
C)
D)

Question 50

User row operations to change the matrix to reduced form.

A)
B)
C)
D)

Question 51

Write the linear system corresponding to the reduced augmented matrix.

A) x1 = -4, x2 = t + 6, x3 = t for any real number t
B) x1 = 4, x2 = t + 6, x3 = 0
C) No Solution
D) x1 = 4, x2 = -t + 6, x3 = t for any real number t

Question 52

Find the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM.
If $9,000 is to be invested, part at 13% and the rest at 8% simple interest, how much should be invested at each
rate so that the total annual return will be the same as $9,000 invested at 9%? Set up a system of linear
equations, letting x1 be the amount invested at 13% and t 13% and be the amount invested at 8%.

Question 53

Solve the problem.
Linda invests $25,000 for one year. Part is invested at 5%, another part at 6%, and the rest at 8%. The total income from all 3 investments is $1600. The income from the 5% and 6% investments is the same as the income
From the 8% investment. Find the amount invested at each rate.

A) $10,000 at 5%, $10,000 at 6%, $5000 at 8%
B) $10,000 at 5%, $5000 at 6%, $10,000 at 8%
C) $8000 at 5%, $10,000 at 6%, $7000 at 8%
D) $5000 at 5%, $10,000 at 6%, $10,000 at 8%

Question 54

User row operations to change the matrix to reduced form.

A)
B)
C)
D)

Question 55

Find the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM.
A paper company produces high, medium, and low grade paper. The number of tons of each grade that is produced
from one ton of pulp depends on the source of that pulp. The following table lists three sources and the amount of each
grade of paper that can be made for one ton of pulp from each source. The paper company has orders for 11 tons of high grade, 15 tons of medium grade, and 14 tons of low grade paper.
How many tons of each type of pulp should be used to fill these orders exactly? Set up a system of linear equations,
letting x, y, and z be the number of tons of Brazilian pulp, domestic pulp, and recycled pulp, respectively, needed to fill
the orders.

Question 56

Solve the problem.
A trucking firm wants to purchase 10 trucks that will provide exactly 28 tons of additional shipping capacity. A
model A truck holds 2 tons, a model B truck holds 3 tons, and a model C truck holds 5 tons. How many trucks
of each model should the company purchase to provide the additional shipping capacity? Set up a system of
linear equations and solve using Gauss-Jordan elimination. There may be more than one solution.

Question 57

Solve using Gauss-Jordan elimination.
2

A)
B) (-1, -1)
C) (-9, -3)
D) No solution

Question 58

Find the system of equations to model the problem. DO NOT SOLVE THIS SYSTEM.
Labor and material costs for manufacturing each of three types of products M, N, and P are given in the table:
Product The weekly allocation for labor is $50,000 and for materials is $80,000. There are to be 3 times as many units of product
M manufactured as units of product P. How many of each type of product would be manufactured each week to use
exactly each of the weekly allocations? Set up a system of linear equations, letting x1, x2, and x3 be the number
of units of products M, N, and P, respectively, manufactured in one week.

Question 59

Solve the problem.
A hospital dietitian wants to insure that a certain meal consisting of rice, broccoli, and fish contains exactly
26,800 units of vitamin A, 840 units of vitamin E, and 11,160 units of vitamin C. One ounce of rice contains 400
units of vitamin A, 20 units of vitamin E, and 180 units of vitamin C. One ounce of broccoli contains 800 units of
vitamin A, 60 units of vitamin E, and 540 units of vitamin C. And one ounce of fish contains 2,400 units of
vitamin A, 40 units of vitamin E, and 810 units of vitamin C. How many ounces of each food should this meal
include? Set up a system of linear equations and solve using Gauss-Jordan elimination.

Question 60

Solve using Gauss-Jordan elimination.

A) (4, -2, 5)
B) (5, -2, 4)
C) (5, 4, -2)
D) No solution

Question 61

Perform the operation, if possible.
-- 2

A) - 43 3 2
B)
C)
D)

Question 62

Perform the indicated operations given the matrices.
Let A = an ad B = ;; 2A + 3B

A)
B)
C)
D)

Question 63

Perform the operation, if possible.
Let C = and D and D= . . Find C - 4D.

A)
B)
C)
D)

Question 64

Perform the operation, if possible.
Let A == a and B = . Fi. Fnd AB.

Question 65

Solve the problem.
A company makes three chocolate candies: cherry, almond, and raisin. Matrix A gives the number of units of each ingredient in each type of candy in one batch. Matrix B gives the cost of each ingredient (dollars per unit)
From suppliers X and Y. What is the cost of 100 batches from supplier X?

A) $3300
B) $6600
C) $7800
D) $4800

Question 66

Find the values of a, b, c, and d that make the matrix equation true.

A)
B)
C)
D)

Question 67

Find the values of a, b, c, and d that make the matrix equation true.

A)
B)
C)
D)

Question 68

Solve the problem.
A Dawn Bakery bakes whole wheat, oat, and rye bread, with mixing, baking, and packaging times, in hours, as shown: An order is received for 400 loaves of whole wheat bread, 200 loaves of oat bread, and 350 loaves of rye bread. Given that the cost of mixing, baking, and packaging is $14, $25, and$2, respectively, per hour, find matrices B and C so that the
Product BAC will give the total cost (excluding raw materials) of filling this order. Find the total cost.

A)
B)
C)
D)

Question 69

Perform the operation, if possible.

A)
B)
C)
D)

Question 70

Perform the operation, if possible.

A)
B)
C)
D) Not defined

Question 71

Perform the operation, if possible.
Let A = an ad B = . Fi Fnd BA.

Question 72

Perform the indicated operations given the matrices.
Let A =

A)
B)
C)
D)

Question 73

Perform the operation, if possible.
Let B = -1 6 7 -3 . Find -2B.

A) 2 -12 -14 6
B) -3 4 5 -5
C) -2 12 14 -6
D) 2 6 7 -3

Question 74

Provide an appropriate response.
Given A = , determine determinewhich of the following products is NOT defined.

A) DB
B) BC
C) DA
D) AD

Question 75

Perform the operation, if possible.
A =

A)
B) BA is not defined.
C)
D)

Question 76

Perform the indicated operations given the matrices.
Let C = and D = ; C - 3D

A)
B)
C)
D)

Question 77

Perform the operation, if possible.
Let A = an ad B = . Fi. Fnd AB.

A)
B)
C)
D)

Question 78

Perform the operation, if possible.
If a and b are nonzero real numbers and A =

Question 79

Perform the operation, if possible.
Let A = an ad B = . . Find A + B.

A)
B)
C)
D)

Question 80

Perform the operation, if possible.
A = , B , B = Find AB.

A)
B)
C)
D)