Q1. On a summer day, the bottom water of a lake is at a temperature of 5 Celsius. What is this temperature in Fahrenheit?

a. 37

b. 5

c. 41

d. 9

Q2. Which cost function for the problem. Assume that the relationship is linear.

A cab company charges a base rate of $1.00 plus 10 cents per minute. Let C(x) be the cost in dollars of using the cab for x minutes.

a. C(x) = 1.00x - 0.10

b. C(x) = 0.10x + 1.00

c. C(x) = 1.00x + 0.10

d. C(x) = 0.10x - 1.00

Q3. A shoe company will make a new type of shoe. The fixed cost for the production will be $24,000. The variable cost will be $35 per pair of shoes. The shoes will sell for $105 for each pair. How many pairs of shoes will have to be sold for the company to break even on this new line of shoes?

a. 686 pairs

b. 70 pairs

c. 343 pairs

d. 229 pairs

Q4. Midtown Delivery Service delivers packages which cost $1.30 per package to deliver. The fixed cost to run the delivery truck is $105.00 per day. If the company charges $6.30 per package, how many packages must be delivered daily to break even?

a. 80 packages

b. 21 packages

c. 13 packages

d. 14 packages

Q5. Midtown Delivery Service delivers packages which cost $2.30 per package to deliver. The fixed cost to run the delivery truck is $122.00 per day. If the company charges $4.30 per package, how many packages must be delivered daily to make a profit of $26.00?

a. 74 packages

b. 18 packages

c. 53 packages

d. 61 packages

Q6. which cost function for the problem. Assume that the relationship is linear.

Marginal cost, $30; 90 items cost $3500 to produce

a. C(x) = 30x + 3500

b. C(x) = 30x + 800

c. C(x) = 9x + 800

d. C(x) = 9x + 3500

Q7. The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test. Use the equation of the least squares line to predict the score on the test of a student who studies 12 hours.

a. 80.1

b. 85.1

c. 75.1

d. 85.3

Q8. Midtown Delivery Service delivers packages which cost $2.50 per package to deliver. The fixed cost to run the delivery truck is $185.00 per day. If the company charges $7.50 per package, how many packages must be delivered daily to make a profit of $75.00

a. 18 packages

b. 74 packages

c. 37 packages

d. 52 packages

Q9. The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands). Use the equation of the least squares line to predict the number of products sold if the cost of advertising is $10,000.

a. 80.7

b. 90.4

c. 27,955.8

d. 83.7

Q10. Which equation for the line. Use slope-intercept form, if possible.

Through (0, 2), m =

a. y = -x + 2

b. y = -x - 2

c. y =x - 2

d. y =x + 2

Q11. Perform the indicated operation where possible.^-

a.

b.

c.

d. Not possible

Q12. Use the echelon method to solve the system of two equations in two unknowns.

x + 2y = -7

-7x + 3y = 49

a. (-6, -7)

b. (-7, 0)

c. (7, -1)

d. No solution

Q13. Use a graphing calculator to solve the system of equations. Round your solution to one decimal place.

2.5x + 1.5y - 3.9z = 2.8

5.8x - 6.5y + 0.6z = -4.9

2.0x + 3.1y + 4.0z = 8.3

a. (1.7, 3.1, 0.9)

b. (3.4, 6.2, 1.7)

c. (0.4, 0.8, 0.2)

d. (0.9, 1.6, 0.4)

Q14. Use the echelon method to solve the system of three equations in three unknowns.

4x + 5y + z = -33

2x - 2y - z = -3

4x + y + 2z = -14

a. (-4, 3, -4)

b. (3, -4, -4)

c. (-4, -4, 3)

d. No solution

Q15. Use the echelon method to solve the system.

-=

+=

a.

b.

c.

d.

Q16. Use the Gauss-Jordan method to solve the system of equations.

7x - y - 3z = -21

-4x + 7y - 9z = -33

-4x - 5y + z = -39

a. (-2, 8, 4)

b. (2, 9, 8)

c. (2, 8, 9)

d. No solution

Q17. Anne and Nancy use a metal alloy that is 28% copper to make jewelry. How many ounces of a 24% alloy must be mixed with a 30% alloy to form 111 ounces of the desired alloy?

a. 37 ounces

b. 74 ounces

c. 79 ounces

d. 39 ounces

Q18. Write the system of equations associated with the augmented matrix.

a. x = 3; y = 10; z = -4

b. x = 0; y = 13; z = -1

c. x = 7; y = 14; z = 0

d. x = -3; y =-10; z = 4

Q19. Solve the system of equations by using the inverse of the coefficient matrix.

x - y + 5z = -11

5x + z = -2

x + 4y + z = 2

a. (-2, 0, 1)

b. (0, 1, -2)

c. (-2, 1, 0)

d. No inverse, no solution for system

Q20. Solve the system of equations by using the inverse of the coefficient matrix.

-2x - 6y = -2

2x - y = -5

a. (-1, 2)

b. (-2, 1)

c. (2, -1)

d. (1, -2)

Q21. Graph the linear inequality.

x + y < -2

a.

b.

c.

d.

Q22. Use the indicated region of feasible solutions to find the maximum and minimum values of the given objective function.

z = 19x - 21y

a. Maximum of -126; minimum of 0

b. Maximum of -81.25; minimum of -126

c. Maximum of 95; minimum of 0

d. Maximum of 95; minimum of -126

Q23. A certain area of forest is populated by two species of animals, which scientists refer to as A and B for simplicity. The forest supplies two kinds of food, referred to as F₁and F₂. For one year, species A requires 1.35 units of F₁and 1.2 units of F₂. Species B requires 2.2 units of F₁and 1.8 units of F₂. The forest can normally supply at most 830 units of F₁and 488 units of F₂per year. What is the maximum total number of these animals that the forest can support?

a. 976 animals

b. 191 animals

c. 406 animals

d. 361 animals

Q24. An airline with two types of airplanes, P₁and P₂, has contracted with a tour group to provide transportation for a minimum of 400 first class, 750 tourist class, and 1500 economy class passengers. For a certain trip, airplane P₁costs $10,000 to operate and can accommodate 20 first class, 50 tourist class, and 110 economy class passengers. Airplane P₂costs $8500 to operate and can accommodate 18 first class, 30 tourist class, and 44 economy class passengers. How many of each type of airplane should be used in order to minimize the operating cost?

a. 11 P₁planes and 7 P₂planes

b. 7 P₁planes and 11 P₂planes

c. 5 P₁planes and 17 P₂planes

d. 9 P₁planes and 13 P₂planes

Q25. A company makes two kinds of engineering pencils, Type I and Type II (deluxe). Type I needs 2 min of sanding and 6 min of polishing. Type II needs 5 min of sanding and 3 min of polishing. The sander can run no more than 66 hours per week and the polisher can run no more than 73 hours a week. A $3 profit is made on Type I and $5 profit on Type II. How many of each type should be made to maximize profits?

a. 400 Type I, 712 Type II

b. 730 Type I, 0 Type II

c. 0 Type I, 792 Type II

d. 417 Type I, 625 Type II

Q26. An airline with two types of airplanes, P₁and P₂, has contracted with a tour group to provide transportation for a minimum of 400 first class, 900 tourist class, and 1500 economy class passengers. For a certain trip, airplane P₁costs $10,000 to operate and can accomodate 20 first class, 50 tourist class, and 110 economy class passengers. Airplane P₂costs $8500 to operate and can accomodate 18 first class, 30 tourist class, and 44 economy class passengers. How many of each type of airplane should be used in order to minimize the operating cost?

a. 9 P₁planes and 13 P₂planes

b. 5 P₁planes and 22 P₂planes

c. 13 P₁planes and 9 P₂planes

d. 14 P₁planes and 7 P₂planes

Q27. Use the indicated region of feasible solutions to find the maximum and minimum values of the given objective function.

z = 6x - 8y

a. Maximum of -32.5; minimum of -48

b. Maximum of 30; minimum of 0

c. Maximum of -48; minimum of 0

d. Maximum of 30; minimum of -48

Q28. Provide an appropriate response.

Is it possible that the feasible region of a linear program include more than one distinct area?

a. No

b. Yes

Q29. Use the indicated region of feasible solutions to find the maximum and minimum values of the given objective function.

z = 21x + 5y + 12

a. No maximum; minimum of 17

b. No maximum; minimum of 12

c. No maximum; minimum of 33

d. No maximum; minimum of 38

Q30. A certain area of forest is populated by two species of animals, which scientists refer to as A and B for simplicity. The forest supplies two kinds of food, referred to as F₁and F₂. For one year, species A requires 1.25000002 units of F₁and 1.00000001 units of F₂. Species B requires 2.1 units of F₁and 1.9 units of F₂. The forest can normally supply at most 985 units of F₁and 468 units of F₂per year. What is the maximum total number of these animals that the forest can support?

a. 1162 animals

b. 374 animals

c. 207 animals

d. 467 animals

Q31. Pivot once about the circled element in the simplex tableau, and read the solution from the result.

a. x₃= 14, s₂= 12, s₃= -4, z = 42; x₁, x₂, s₁= 0

b. x₃= 14, s₂= 12, s₃= 4, z = 42; x₁, x₂, s₁= 0

c. x₃= 14, s₂= -12, s₃= 4, z = -42; x₁, x₂, s₁= 0

d. x₃= 14, s₂= -6, s₃= 4, z = 42; x₁, x₂, s₁= 0

Q32. A toy making company has at least 300 squares of felt, 700 oz of stuffing, and 230 ft of trim to make dogs and dinosaurs. A dog uses 1 square of felt, 4 oz of stuffing, and 1 ft of trim. A dinosaur uses 2 squares of felt, 3 oz of stuffing, and 1 ft of trim.

It costs the company $1.65 to make each dog and $1.52 for each dinosaur. What is the company's minimum cost?

a. $228

b. $317

c. $289

d. $362

Q33. A toy making company has at least 300 squares of felt, 700 oz of stuffing, and 230 ft of trim to make dogs and dinosaurs. A dog uses 1 square of felt, 4 oz of stuffing, and 1 ft of trim. A dinosaur uses 2 squares of felt, 3 oz of stuffing, and 1 ft of trim.

It costs the company $1.72 to make each dog and $1.88 for each dinosaur. The company wants to minimize its costs. What are the coefficients of the objective function?

a. 1, 4, 1

b. 300, 700, 230

c. 2, 3, 1

d. 1.72, 1.88

Q34. A toy making company has at least 300 squares of felt, 700 oz of stuffing, and 230 ft of trim to make dogs and dinosaurs. A dog uses 1 square of felt, 4 oz of stuffing, and 1 ft of trim. A dinosaur uses 2 squares of felt, 3 oz of stuffing, and 1 ft of trim.

It costs the company $1.63 to make each dog and $1.92 for each dinosaur. The company wants to minimize its costs. What are the coefficients of the dual objective function?

a. 1, 2, 1.63

b. 300, 700, 230

c. 1, 4, 1

d. 1.63, 1.92

Q35. A toy making company has at least 300 squares of felt, 700 oz of stuffing, and 230 ft of trim to make dogs and dinosaurs. A dog uses 1 square of felt, 4 oz of stuffing, and 1 ft of trim. A dinosaur uses 2 squares of felt, 3 oz of stuffing, and 1 ft of trim.

It costs the company $1.62 to make each dog and $1.83 for each dinosaur. The company wants to minimize its costs. What are the coefficients of the constraint inequality for trim?

a. 1, 2

b. 1, 1

c. 4, 3

d. 1.62, 1.83

Q36. An appliance store sells two types of refrigerators. Each Cool-It refrigerator sells for $540 and each Polar sells for $780. Up to 320 refrigerators can be stored in the warehouse and new refrigerators are delivered only once a month. It is known that customers will buy at least 60 Cool-Its and at least 120 Polars each month. How many of each brand should the store stock and sell each month to maximize revenues?

a. 75 Cool-Its and 245 Polars

b. 200 Cool-Its and 120 Polars

c. 60 Cool-Its and 260 Polars

d. 260 Cool-Its and 190 Polars

Q37. A toy making company has at least 300 squares of felt, 700 oz of stuffing, and 230 ft of trim to make dogs and dinosaurs. A dog uses 1 square of felt, 4 oz of stuffing, and 1 ft of trim. A dinosaur uses 2 squares of felt, 3 oz of stuffing, and 1 ft of trim.

It costs the company $1.98 to make each dog and $1.01 for each dinosaur. What is the company's minimum cost?

a. $151.5

b. $373

c. $347

d. $299

Q38. Find the transpose of the matrix.

a.

b.

c.

d.

Q39. Pivot once about the circled element in the simplex tableau, and read the solution from the result.

a. x₁= 48, s₂= -16, z = -48; x₂, x₃, s₁= 0

b. x₁= 24, s₂= -16, z = -24; x₂, x₃, s₂= 0

c. x₁= 48, s₂= 16, z = 48; x₂, x₃, s₁= 0

d. x₁= 24, s₂= -16, z = 24; x₂, x₃, s₁= 0

Q40. An appliance store sells two types of refrigerators. Each Cool-It refrigerator sells for $640 and each Polar sells for $780. Up to 250 refrigerators can be stored in the warehouse and new refrigerators are delivered only once a month. It is known that customers will buy at least 80 Cool-Its and at least 120 Polars each month. How many of each brand should the store stock and sell each month to maximize revenues?

a. 95 Cool-Its and 155 Polars

b. 210 Cool-Its and 145 Polars

c. 130 Cool-Its and 120 Polars

d. 80 Cool-Its and 170 Polars

Q41. The Habers purchase a $6,500 living room set and take out a two-year loan for the entire amount at 26% with monthly payments. After 14 of 24 installments, they decide to pay it off. How much do they save in interest? How much is needed to pay the balance of the loan?

a. $383.53, $3,118.27

b. $1,904.32, $4,902.52

c. $350.18, $8,404.32

d. $1,520.79, $3,381.73

Q42. A small company borrows $79,000 at 11% compounded monthly. The loan is due in 9 years. How much interest will the company pay?

a. $130,728.32

b. $130,784.30

c. $132,650.83

d. $211,650.83

Q43. Felipe Rivera's savings account has a balance of $2152. After 2 years what will the amount of interest be at 9% compounded quarterly?

a. $424.28

b. $419.28

c. $96.84

d. $410.28

Q44. June made an initial deposit of $4300 in an account for her son. Assuming an interest rate of 8% compounded quarterly, how much will the account be worth in 19 years?

a. $18,988.09

b. $19,367.85

c. $19,086.90

d. $9308.40

Q45. Find the amount that should be invested now to accumulate the following amount, if the money is compounded as indicated.

$6800 at 7% compounded annually for 7 yr.

a. $4531.13

b. $2565.30

c. $10,919.31

d. $4234.70

Q46. How long will it take for prices in the economy to double at a 2% annual inflation rate? Round answer to the nearest year.

a. 36 years

b. 13 years

c. 25 years

d. 45 years

Q47. Find the amount that should be invested now to accumulate the following amount, if the money is compounded as indicated.

$5400 at 6% compounded quarterly for 7 yr

a. $8193.00

b. $3591.31

c. $3559.14

d. $1840.86

Q48. Find the indicated term of the geometric sequence.

a = 3, r = 2; Find the 14th term.

a. 24,576

b. 49,152

c. 98,304

d. 8192

Q49. Find the compound amount for the deposit. Round to the nearest cent.

$5000 at 10% compounded semiannually for 10 years

a. $8144.47

b. $13,266.49

c. $12,968.71

d. $10,000.00

Q50. Find the compound amount for the deposit. Round to the nearest cent.

$1370 at 11% compounded annually for 5 years

a. $2123.50

b. $2308.53

c. $1972.80

d. $2079.76