Free Printable Mansci tb chapter 1 — Accounting (Far Eastern University)

1.

True/False: The process of decision making is more limited than that of problem solving.

a)

True

b)

False

2.

True/False: The breakeven point is the point at which the volume of output produced is the result of total revenue equaling total cost.

a)

True

b)

False

3.

True/False: Problem solving encompasses both the identification of a problem and the action to resolve it.

a)

True

b)

False

4.

True/False: The decision-making process includes implementation and subsequent evaluation of the decision.

a)

True

b)

False

5.

True/False: Most successful quantitative analysis models will advise separating the management analyst from the managerial team until after the problem has been fully structured.

a)

True

b)

False

6.

True/False: The value of making a decision based on models is dependent on how closely the model represents the real situation.

a)

True

b)

False

7.

True/False: Uncontrollable inputs are the decision variables for a model.

a)

True

b)

False

8.

True/False: The feasible solution is the best solution possible for a mathematical model.

a)

True

b)

False

9.

True/False: Frederic W. Taylor is credited with providing the foundation for quantitative methodology in the early part of the 20th century.

a)

True

b)

False

10.

True/False: To identify the choice that provides the highest profit and also uses the fewest employees, we apply a single-criterion decision process.

a)

True

b)

False

11.

True/False: The most critical component in determining the success or failure of any quantitative approach to decision making is problem definition.

a)

True

b)

False

12.

True/False: The first step in the decision-making process is to identify the problem.

a)

True

b)

False

13.

True/False: All uncontrollable inputs or data must be specified before we can analyze the model and recommend a decision or solution for the problem.

a)

True

b)

False

14.

True/False: If you are deciding to buy either machine A, B, or C with the objective of minimizing the sum of labor, material and utility costs, you are dealing with a single-criterion decision.

a)

True

b)

False

15.

True/False: Model development should be left to quantitative analysts; the model user's involvement should begin at the implementation stage.

a)

True

b)

False

16.

True/False: A feasible solution is one that satisfies at least one of the constraints in the problem.

a)

True

b)

False

17.

True/False: A toy train layout designed to represent an actual railyard is an example of an analog model.

a)

True

b)

False

18.

True/False: The last step in any problem-solving process is to choose the correct alternative among those available.

a)

True

b)

False

19.

True/False: Decision variables in a production process are those that cannot be controlled by the manager.

a)

True

b)

False

20.

True/False: The optimal solution to a model is one in which known, specific values provide the best output.

a)

True

b)

False

21.

If all the uncontrollable inputs into the decision-making process are known to the decision maker, the model of decision making is known as "stochastic."

a)

True

b)

False

22.

The field of management science

a)

concentrates on the use of quantitative methods to assist in decision making.

b)

approaches decision making rationally, with techniques based on the scientific method.

c)

is another name for decision science and for operations research.

d)

All of these are correct.

23.

By identifying and defining a problem, we have

a)

taken the final step in the decision-making process.

b)

proposed all viable alternatives.

c)

considered multiple criteria.

d)

taken the first step of decision making.

24.

The set of decision alternatives

a)

should be identified before the decision criteria are established.

b)

are limited to quantitative solutions.

c)

are evaluated as a part of the problem definition stage.

d)

are best generated by brainstorming.

25.

Decision criteria

a)

are the choices faced by the decision maker.

b)

are the problems faced by the decision maker.

c)

are the ways to evaluate the choices faced by the decision maker.

d)

are unique for any problem.

26.

In a multicriteria decision problem

a)

it is impossible to select a single decision alternative.

b)

the decision maker must evaluate each alternative with respect to each criterion.

c)

successive decisions must be made over time.

d)

All of these are correct.

27.

The quantitative analysis approach requires

a)

the manager's prior experience with a similar problem.

b)

a relatively uncomplicated problem.

c)

mathematical expressions for the relationships.

d)

All of these are correct.

28.

A thermometer is an example of a model that does not have the same physical appearance as that which is being modeled; thus, it is a(n)

a)

analog model.

b)

iconic model.

c)

mathematical model.

d)

qualitative model.

29.

Inputs to a quantitative model

a)

are a trivial part of the problem solving process.

b)

are uncertain for a stochastic model.

c)

are uncontrollable for the decision variables.

d)

must all be deterministic if the problem is to have a solution.

30.

When the value of the output cannot be determined even if the value of the controllable input is known, the model is

a)

analog.

b)

digital.

c)

stochastic.

d)

deterministic.

31.

The volume that results in total revenue being equal to total cost is known as the

a)

breakeven point.

b)

marginal volume.

c)

marginal cost.

d)

profit mix.

32.

Management science and operations research both involve

a)

qualitative managerial skills.

b)

quantitative approaches to decision making.

c)

operational management skills.

d)

scientific research as opposed to applications.

33.

George Dantzig is important in the history of management science because he developed

a)

the scientific management revolution.

b)

World War II operations research teams.

c)

the simplex method for linear programming.

d)

powerful digital computers.

34.

In order to undertake problem solving, the first step must be

a)

the determination of the correct analytical solution procedure.

b)

the definition of decision variables.

c)

the identification of a difference between the actual and desired state of affairs.

d)

None of these are correct.

35.

The process of problem definition must

a)

include specific objectives and operating constraints.

b)

occur prior to the quantitative analysis process.

c)

involve both the analyst and the user of the results.

d)

All of these are correct.

36.

A model that uses a system of symbols or expressions to represent a problem is called a(n) ______ model.

a)

mathematical

b)

iconic

c)

analog

d)

constrained

37.

Which of the following is NOT one of the commonly used names for the body of knowledge involving quantitative approaches to decision making?

a)

management science

b)

operations research

c)

scientific management

d)

decision science

38.

A valid reason for using a quantitative approach to the decision-making process is when

a)

the problem is repetitive, necessitating routine decision making.

b)

the problem is unique and the manager has no prior experience solving this sort of problem.

c)

the problem is particularly complex.

d)

All of these are correct.

39.

A snack food manufacturer buys corn for tortilla chips from two cooperatives, one in Iowa and one in Illinois. The price per unit of the Iowa corn is $6.00 and the price per unit of the Illinois corn is$ 5.50. Define variables that would tell how many units to purchase from each source.

a)

Let x1 = the number of units from Iowa; let x2 = the number of units from Illinois.

b)

Let x1 = the number of units from Illinois; let x2 = the number of units from Iowa.

c)

Let x1 = total units; let x2 = average units per source.

d)

Let x1 = cost from Iowa; let x2 = cost from Illinois.

40.

A snack food manufacturer buys corn for tortilla chips from two cooperatives, one in Iowa and one in Illinois. The price per unit of the Iowa corn is $6.00 and the price per unit of the Illinois corn is$ 5.50. Develop an objective function that would minimize the total cost.

a)

Min 6x1 + 5.5x2

b)

Min 5.5x1 + 6x2

c)

Min 6(x1 + x2)

d)

Min 5.5(x1 + x2)

41.

A snack food manufacturer needs at least 12,000 units of corn. The Iowa cooperative can supply up to 8000 units, and the Illinois cooperative can supply at least 6000 units. Develop constraints for these conditions.

a)

x1 + x2 ≥ 12,000

b)

x1 ≤ 8,000

c)

x2 ≥ 6,000

d)

x1 ≥ 8,000

42.

The relationship d = 5000 − 25p describes what happens to demand d as price p varies, where price can vary between $10 and$ 50. How many units can be sold at the $10 price, and how many can be sold at the$ 50 price?

a)

$p$ $=$ $10$ gives $d$ $=$ $4750$ ; $p$ $=$ $50$ gives $d$ $=$ $3750$

b)

$p$ $=$ $10$ gives $d$ $=$ $5000$ ; $p$ $=$ $50$ gives $d$ $=$ $2500$

c)

$p$ $=$ $10$ gives $d$ $=$ $4500$ ; $p$ $=$ $50$ gives $d$ $=$ $4000$

d)

$p$ $=$ $10$ gives $d$ $=$ $3750$ ; $p$ $=$ $50$ gives $d$ $=$ $4750$

43.

Using d = 5000 − 25p, model the expression for total revenue.

a)

TR = p(5000 − 25p)

b)

TR = 5000p − 25

c)

TR = 25p − 5000

d)

TR = 5000 − 25p

44.

Using d = 5000 − 25p, consider prices of $20,$ 30, and $40. Which of these three price alternatives will maximize total revenue, and what are the values for demand and revenue at this price?

a)

$p$ $=$ $40$ , $d$ $=$ $4000$ , TR $=$ $160{,}000$

b)

$p$ $=$ $30$ , $d$ $=$ $4250$ , TR $=$ $127{,}500$

c)

$p$ $=$ $20$ , $d$ $=$ $4500$ , TR $=$ $90{,}000$

d)

All three prices yield the same total revenue.

45.

There is a fixed cost of $50,000 to start a production process. Once the process has begun, the variable cost per unit is$ 25. The revenue per unit is projected to be $45. Write an expression for total cost.

a)

C(x) = 50000 + 25x

b)

C(x) = 25x

c)

C(x) = 50000x + 25

d)

C(x) = 45x − 25

46.

There is a fixed cost of $50,000 to start a production process. Once the process has begun, the variable cost per unit is$ 25. The revenue per unit is projected to be $45. Write an expression for total revenue.

a)

R(x) = 45x

b)

R(x) = 50000 + 45x

c)

R(x) = 45x − (50000 + 25x)

d)

R(x) = 25x

47.

There is a fixed cost of $50,000 to start a production process. Once the process has begun, the variable cost per unit is$ 25. The revenue per unit is projected to be $45. Write an expression for total profit.

a)

P(x) = 45x − (50000 + 25x)

b)

P(x) = 45x

c)

P(x) = 50000 + 25x

d)

P(x) = 25x − 45x

48.

There is a fixed cost of $50,000 to start a production process. Once the process has begun, the variable cost per unit is$ 25. The revenue per unit is projected to be $45. Find the breakeven point.

a)

$x$ $=$ $2500$

b)

$x$ $=$ $50000$

c)

$x$ $=$ $2000$

d)

$x$ $=$ $1800$

49.

An author has received an advance against royalties of $10,000. The royalty rate is$ 1.00 for every book sold in the United States, and $1.35 for every book sold outside the United States. Define variables for this problem and write an expression that could be used to calculate the number of books to be sold to cover the advance.

a)

Let x1 be the number of books sold in the U.S. and x2 be the number sold outside the U.S.; $10000$ $=$ $1x1$ $+$ $1.35x2$

b)

Let x1 be dollars of royalties in the U.S. and x2 dollars outside; $x1$ $+$ $x2$ $=$ $10000$

c)

Let x1 be total books and x2 be average price; $x1$ $+$ $1.35x2$ $=$ $10000$

d)

Let x1 be the number of books sold outside the U.S. and x2 be the number sold in the U.S.; $10000$ $=$ $1x2$ $+$ $1.35x1$

50.

A university schedules summer school courses based on anticipated enrollment. The cost for faculty compensation, laboratories, student services, and allocated overhead for a computer class is $8500. If students pay$ 920 to enroll in the course, how large would enrollment have to be for the university to break even?

a)

10 students

b)

9 students

c)

8 students

d)

11 students

51.

As part of their application for a loan to buy Lakeside Farm, a property they hope to develop as a bed-and-breakfast operation, the prospective owners have projected monthly fixed cost (loan payment, taxes, insurance, maintenance) of $6000, variable cost per occupied room per night of$ 20, and revenue per occupied room per night of $75. Write the expression for total cost per month. Assume 30 days per month.

a)

C(x) = 6000 + 20(30)x

b)

C(x) = 6000 + 20x

c)

C(x) = 6000 + 75(30)x

d)

C(x) = 20(30)x

52.

As part of their application for a loan to buy Lakeside Farm, a property they hope to develop as a bed-and-breakfast operation, the prospective owners have projected monthly fixed cost (loan payment, taxes, insurance, maintenance) of $6000, variable cost per occupied room per night of$ 20, and revenue per occupied room per night of $75. Write the expression for total revenue per month. Assume 30 days per month.

a)

R(x) = 75(30)x

b)

R(x) = 6000 + 75(30)x

c)

R(x) = 20(30)x

d)

R(x) = 75x

53.

As part of their application for a loan to buy Lakeside Farm, a property they hope to develop as a bed-and-breakfast operation, the prospective owners have projected monthly fixed cost (loan payment, taxes, insurance, maintenance) of $6000, variable cost per occupied room per night of$ 20, and revenue per occupied room per night of $75. If there are 12 guest rooms available, can they break even? What percentage of rooms would need to be occupied, on average, to break even?

a)

Yes; about 33% occupancy (≈ 3.64 rooms per night)

b)

No; at least 50% occupancy is required

c)

Yes; exactly 25% occupancy is sufficient

d)

No; more than 75% occupancy is required

54.

Organizers of an Internet training session will charge participants $150 to attend. It costs$ 3000 to reserve the room, hire the instructor, bring in the equipment, and advertise. Assume it costs $25 per student for the organizers to provide the course materials. How many students would have to attend for the company to break even?

a)

24

b)

20

c)

30

d)

18

55.

Organizers of an Internet training session will charge participants $150 to attend. It costs$ 3000 to reserve the room, hire the instructor, bring in the equipment, and advertise. Assume it costs $25 per student for the organizers to provide the course materials. If the trainers think, realistically, that 20 people will attend, then what price should be charged per person for the organization to break even?

a)

$175

b)

$150

c)

$165

d)

$200

56.

In this portion of an Excel spreadsheet, the user has given values for selling price, the costs, and a sample volume. Give the cell formula for each item: breakeven volume in cell E12.

a)

=E9/(E6−E10)

b)

=E6/(E9−E10)

c)

=E6*E9

d)

=E9+E10

57.

In this portion of an Excel spreadsheet, the user has given values for selling price, the costs, and a sample volume. Give the cell formula for each item: total revenue in cell E16.

a)

=E15*E6

b)

=E6*E10

c)

=E9+E10*E15

d)

=E16−E17

58.

In this portion of an Excel spreadsheet, the user has given values for selling price, the costs, and a sample volume. Give the cell formula for each item: total cost in cell E17.

a)

=E9+E10*E15

b)

=E15*E6

c)

=E9/(E6−E10)

d)

=E16−E17

59.

In this portion of an Excel spreadsheet, the user has given values for selling price, the costs, and a sample volume. Give the cell formula for each item: profit (loss) in cell E19.

a)

=E16−E17

b)

=E17−E16

c)

=E9+E10

d)

=E15*E6

60.

A furniture store has set aside 800 square feet to display its sofas and chairs. Each sofa utilizes 50 sq. ft. and each chair utilizes 30 sq. ft. At least five sofas and at least five chairs are to be displayed. Write a mathematical model representing the store's constraints.

a)

50s + 30c ≤ 800

b)

s ≥ 5

c)

c ≥ 5

d)

s + c ≤ 800

61.

Suppose the profit on sofas is $200 and on chairs is$ 100. On a given day, the probability that a displayed sofa will be sold is .03 and that a displayed chair will be sold is .05. Mathematically model the following objective: maximize the total pieces of furniture displayed.

a)

Max s + c

b)

Max 50s + 30c

c)

Max 6s + 5c

d)

Max .03s + .05c

62.

Suppose the profit on sofas is $200 and on chairs is$ 100. On a given day, the probability that a displayed sofa will be sold is .03 and that a displayed chair will be sold is .05. Mathematically model the following objective: maximize the total expected number of daily sales.

a)

Max .03s + .05c

b)

Max s + c

c)

Max 6s + 5c

d)

Max 200s + 100c

63.

Suppose the profit on sofas is $200 and on chairs is$ 100. On a given day, the probability that a displayed sofa will be sold is .03 and that a displayed chair will be sold is .05. Mathematically model the following objective: maximize the total expected daily profit.

a)

Max 6s + 5c

b)

Max .03s + .05c

c)

Max s + c

d)

Max 200s + 100c

64.

A manufacturer makes two products, doors and windows. Each must be processed through two work areas. Work area #1 has 60 hours of available production time per week. Work area #2 has 48 hours of available production time per week. Manufacturing of a door requires 4 hours in work area #1 and 2 hours in work area #2. Manufacturing of a window requires 2 hours in work area #1 and 4 hours in work area #2. Profit is $8 per door and$ 6 per window. Define decision variables that will tell how many units to build per week.

a)

Let D = the number of doors to build per week; let N = the number of windows to build per week.

b)

Let D = dollars of profit from doors per week; let N = dollars of profit from windows per week.

c)

Let D = total hours in area #1; let N = total hours in area #2.

d)

Let D = the number of doors to build per day; let N = the number of windows to build per day.

65.

A manufacturer makes two products, doors and windows. Each must be processed through two work areas. Work area #1 has 60 hours of available production time per week. Work area #2 has 48 hours of available production time per week. Manufacturing of a door requires 4 hours in work area #1 and 2 hours in work area #2. Manufacturing of a window requires 2 hours in work area #1 and 4 hours in work area #2. Profit is $8 per door and$ 6 per window. Develop an objective function that will maximize total profit per week.

a)

Max 8D + 6W

b)

Max 6D + 8W

c)

Max 4D + 2W

d)

Max 2D + 4W

66.

A manufacturer makes two products, doors and windows. Each must be processed through two work areas. Work area #1 has 60 hours of available production time per week. Work area #2 has 48 hours of available production time per week. Manufacturing of a door requires 4 hours in work area #1 and 2 hours in work area #2. Manufacturing of a window requires 2 hours in work area #1 and 4 hours in work area #2. Develop production constraints for work area #1 and work area #2.

a)

4D + 2W ≤ 60

b)

2D + 4W ≤ 48

c)

D + W ≤ 108

d)

8D + 6W ≤ 60

67.

A firm builds and sells small, ergonomic conference tables. The investment in plant and equipment is $165,000. The variable cost per table is$ 1,500. The selling price of each table is $3,000. How many tables would have to be sold to break even?

a)

110

b)

100

c)

90

d)

120

68.

A computer rework center has the capacity to rework 300 computers per day. The expected number of computers needing to be reworked per day is 225. The center is paid $26 for each computer reworked. The fixed cost of renting the reworking equipment is$ 250 per day. Work space rents for $150 per day. The cost of material is$ 18 per computer and labor costs $3 per computer. What is the breakeven number of computers reworked per day?

a)

60 computers

b)

80 computers

c)

100 computers

d)

120 computers

69.

A driver education school faces the following economics. Annual fixed costs to operate the school are $30,000. The annual cost per car is$ 3,000. The annual cost per instructor is $11,000 and one instructor is needed for each car. Tuition for each student is$ 350. Let x be the number of cars and y be the number of students. Which expression correctly gives total cost?

a)

C(x) = 30000 + 14000x

b)

C(x) = 30000 + 11000x

c)

C(x) = 30000 + 3000x

d)

C(x) = 14000 + 30000x

70.

For the same driver education school, which expression correctly gives total revenue in terms of the number of students y?

a)

R(y) = 350y

b)

R(y) = 30000 + 350y

c)

R(y) = 14000y

d)

R(y) = 350x

71.

For the same driver education school, which expression correctly gives total profit in terms of x (cars) and y (students)?

a)

P(x,y) = 350y − (30000 + 14000x)

b)

P(x,y) = 30000 + 14000x − 350y

c)

P(x,y) = 350x − (30000 + 14000y)

d)

P(x,y) = 350(x+y) − 30000

72.

The school offers the course eight times each year, with two sessions each time. If they operate five cars and four students can be assigned to each car, will they break even under the economics described?

a)

Yes, they can reach breakeven.

b)

No, they cannot reach breakeven.

73.

Zipco Printing operates a shop that has five printing machines with differing processing times by job and operator skill. At the start of the workday there are five printing jobs to schedule. The manager must decide the job–machine assignments. Which analytical approach should be used to decide the assignments so total job processing time is minimized?

a)

A quantitative approach to decision making

b)

A qualitative approach based on operator preferences

c)

Random assignment of jobs to machines

d)

First-come, first-served without analysis

74.

For the same scheduling problem, which uncontrollable inputs should be collected to build the model?

a)

Processing times for each job on each machine

b)

Operator names for each machine

c)

The order in which jobs arrived

d)

Daily shop opening and closing times

75.

In the printing-job scheduling model, which objective function is appropriate?

a)

Minimize total job processing time

b)

Maximize the number of machines used

c)

Minimize the number of jobs

d)

Maximize operator idle time

76.

In the printing-job scheduling model, which description best captures the decision variables?

a)

A binary variable for each job–machine pairing indicating if that pairing is used

b)

A continuous variable giving total shop revenue

c)

A count of operators working on each day

d)

A categorical variable for paper type

77.

In the printing-job scheduling model, which constraint must be included?

a)

Assign each job to exactly one machine and each machine to no more than one job

b)

Limit jobs to machines with the fastest times only

c)

Require all operators to have equal workloads

d)

Force jobs to be scheduled alphabetically

78.

Is the printing-job processing time model deterministic or stochastic in nature?

a)

Stochastic

b)

Deterministic

79.

Which simplifying assumption could be used for the printing-job scheduling problem?

a)

Assume processing times are deterministic (known and fixed)

b)

Assume each operator works different hours every day

c)

Assume jobs can be split across multiple machines simultaneously

d)

Assume machines can process two jobs at once

80.

A department store must ship a product weekly from two warehouses to four stores. Which analytical approach can systematically determine the minimum shipping cost?

a)

A quantitative approach to decision making

b)

A qualitative approach based on manager experience

c)

Random allocation from warehouses

d)

Shipping equal quantities to each store

81.

For the weekly shipping problem, which uncontrollable inputs should be gathered for the model?

a)

Fixed and variable shipping costs; weekly demand at each store; weekly supplies at each warehouse

b)

Store operating hours and staff schedules

c)

Warehouse addresses and phone numbers

d)

The color of shipping boxes

82.

For the weekly shipping problem, which choice best describes the decision variables, objective function, and constraints of the mathematical model?

a)

Decision variables: how much to ship from each warehouse to each store; objective: minimize total shipping cost; constraints: meet store demand without exceeding warehouse supplies

b)

Decision variables: which driver goes to which store; objective: maximize miles driven; constraints: each driver visits only one store

c)

Decision variables: number of trucks owned; objective: minimize truck purchase cost; constraints: at least one truck per warehouse

d)

Decision variables: how long shipments take; objective: minimize time; constraints: no more than two shipments per store

83.

Is the weekly shipping model deterministic or stochastic under realistic conditions?

a)

Stochastic

b)

Deterministic

84.

Which set of assumptions could simplify the weekly shipping model?

a)

Assume fixed shipping cost per item, demand is constant at each store each week, and weekly supplies at warehouses are constant

b)

Assume shipping costs vary randomly by day and demand fluctuates unpredictably

c)

Assume each store has unlimited storage and warehouses have unlimited supply

d)

Assume shipments are made only once per month

85.

Three production processes—A, B, and C—have the following cost structure: Fixed cost per year and variable cost per unit are $120,000 and$ 3.00 for A, $90,000 and$ 4.00 for B, and $80,000 and$ 4.50 for C. For a production volume of 8,000 units, which process is most economical (lowest annual cost)?

a)

Process A

b)

Process B

c)

Process C

d)

All processes have equal cost

86.

For the same three processes, how many units per year must be sold with each process to obtain annual profits of $50,000 when the selling price is$ \ $6.95$ per unit? Choose the correct set.

a)

A: 43,038; B: 47,458; C: 53,062

b)

A: 30,380; B: 30,509; C: 32,654

c)

A: 40,000; B: 45,000; C: 50,000

d)

A: 53,062; B: 47,458; C: 43,038

87.

For the same three processes, what is the breakeven production volume (units per year) for each process? Choose the correct set.

a)

A: 30,380; B: 30,509; C: 32,654

b)

A: 43,038; B: 47,458; C: 53,062

c)

A: 32,654; B: 30,509; C: 30,380

d)

A: 29,470; B: 31,690; C: 33,000

88.

A new printer is to be manufactured at the El Paso plant of Computer Products Corporation (CPC). The plant must choose between an auto‑assembly process and a manual assembly process. Annual fixed cost and variable cost per product are $690,000 and$ 29.56 for auto‑assembly and $269,000 and$ 31.69 for manual assembly. Estimated annual production is 152,000 units in Year 1, 190,000 in Year 2, and 225,000 in Year 3. Which process is the least‑cost alternative in Years 1, 2, and 3?

a)

Year 1: Manual; Year 2: Manual; Year 3: Auto

b)

Year 1: Auto; Year 2: Manual; Year 3: Auto

c)

Year 1: Manual; Year 2: Auto; Year 3: Manual

d)

Year 1: Auto; Year 2: Auto; Year 3: Manual

89.

For Year 2 in the CPC printer decision, what variable cost per unit for the auto‑assembly process would justify its additional fixed cost over the manual assembly process?

a)

$29.47

b)

$29.56

c)

$31.69

d)

$30.00

Mansci tb chapter 1 — Accounting (Far Eastern University)

Total questions: 89

Worksheet time: 45mins

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