business calculations

machines is available for 40 hours a week and there is no setup time required when shifting from the production of one product to any other. The processing requirements to make one unit of each product are shown in the table. Weekly product demand for the next planning period has been forecasted as follows: 80

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E-1000s; 65 S-2000s; 35 P-2000s; and 20 N-1000s.

Processing Time (Minutes Per Printer)

Model Machine

1 Machine 2 Machine 3 Machine 4

E-1000 (E) 10 15 15 5

S-2000 (S) 10 10 10 10

P-2000 (P) 5 10 15 10

N-1000 (N) 5 5 5 10

In the questions that follow, the traditional method refers to maximizing the contribution margin per unit for each product, and the bottleneck method refers to maximizing the contribution margin per minute at the bottleneck for each product.

Use the information in Table 7.6. Using the traditional method, in what sequence should products be scheduled for production?

a. N, S, E, P b. N, E, P, S c. P, E, N, S d. E, S, P, N

Question 3

2.5 out of 2.5 points

In Statistical Process Control, are used to detect defects and determine if the process has deviated from design specifications.

a. Flowcharts

b. Cause-and-Effect Diagrams c. Process Capability Charts

d. Control Charts

Question 4

2.5 out of 2.5 points

The process that facilitates the placement of orders and identifies, attracts, and builds relationships with external customers is called the:

a. customer relationship process.

b. new service development process. c. order fulfillment process.

d. supplier relationship process.

Question 5

Scenario 1.1

2.5 out of 2.5 points

A job consists of three elements. Twenty observations for each element were timed, and the resulting data are shown in the following table. A performance rating has also been assigned for each element, as shown in the table. The job has an allowance of 20% of normal time.

Element

Performance

Rating (%)

Average Element

Time (in minutes)

# 1

80

3.6

# 2

100

2.5

# 3

110

3.1

Use the information in Scenario 1.1. What is the normal time for the entire job?

a. Greater than or equal to 10.0 minutes

b. Less than 10.0 minutes but greater than or equal to 8.5 minutes c. Less than 8.5 minutes but greater than or equal to 7.0 minutes d. Less than 7.0 minutes

Question 6

0 out of 2.5 points

Table 1.3

Act. I.P N. Time C. Time N. COST ($000s) C. COST ($000s) Av. Crash wks C. Cost

/wk

A – 4 2 8 14

B A 3 2 9 11

C A 4 4 10 10

D B,C 5 3 10 15

E C 4 1 11 14

F D,E 1 1 6 6

* Act.: Activity

I.P. : Immediate Predecessor

N. Time : Normal Time

C. Time: Crash Time

N. Cost: Normal Cost ($000s) C. Cost: Crash Cost ($000s)

Av. Crash wks: Available Weeks of Crashing

C. Cost/wk: Crashing cost per week

Which activity should be crashed first for the project shown in Table 1.3?

a. A b. B c. C d. D

Question 7

2.5 out of 2.5 points

You are interested in buying a laptop computer. Your list of considerations include the computer’s speed in processing data, its weight, screen size, and price. You consider a number of different models, and narrow your list based on speed and monitor screen size, then finally select a model to buy based on its weight and price. In this decision, weight and price are examples of:

a. order qualifiers.

b. the voice of the supplier. c. order winners.

d. the voice of the customer.

Question 8

2.5 out of 2.5 points

Input measures to planning long-term capacity include such metrics as:

a. the number of customers served per hour.

b. the number of trucks produced per day. c. the number of machine hours available. d. the number of bills processed in a week.

Question 9

2.5 out of 2.5 points

Regardless of how departments like Accounting, Engineering, Finance, and Marketing function in an organization, they are all linked together through:

a. management. b. processes.

c. customers.

d. stakeholders.

Question 10

2.5 out of 2.5 points

When considering the plan-do-study-act cycle for problem solving, data are collected to measure process improvements in the step.

a. plan b. do

c. study d. act

Question 11 2.5 out of 2.5 points

The upper and lower specifications for a service are 10 min. and 8 min., respectively. The

process average is 9 min. and the process capability ratio is 1.33. What is the process standard deviation?

a. 0.1 b. 0.15 c. 0.20

d. 0.25

Question 12 2.5 out of 2.5 points

Activity slack is defined as:

a. latest start time minus earliest start time. b. earliest start time minus latest start time.

c. earliest finish time minus latest finish time.

d. latest finish time minus earliest start time.

Question 13 2.5 out of 2.5 points

A company desires to set up a line to produce 60 units per hour. The work elements and their precedence relationships are shown in Table 7.12.

Use the information in Table 7.12. What is the highest efficiency line balance possible?

a. Less than 93%

b. More than 93% but less than or equal to 95% c. More than 95% but less than or equal to 97% d. More than 97%

Table 7.12

Work Time Immediate

Page 6 of 17

Element (sec) Predecessor(s)

Question 16

2.5 out of 2.5 points

The second step in Theory of Constraints application, “exploit the bottleneck(s),” means that:

a. the analyst should create a schedule that maximizes the throughput of the bottlenecks.

b. the analyst should repeat the analysis process to look for other bottlenecks.

c. the analyst should consider increasing capacity of the bottleneck.

d. the analyst should schedule non-bottleneck resources to support the bottleneck.

Question 17

2.5 out of 2.5 points

In an assembly operation at a furniture factory, six employees assembled an average of 450 custom cabinet drawers per 5-day week. What is the labor productivity of this operation?

a. 90 chairs per worker per day b. 20 chairs per worker per day c. 15 chairs per worker per day d. 75 chairs per worker per day

Question 18

Front offices typically emphasize:

a. low cost operations and on-time delivery. b. top quality and customization.

c. on-time delivery and standardization. d. top quality and low cost operations

Question 19

Manufacturing processes usually have:

a. physical, durable output.

b. high levels of customer contact.

c. output that cannot be inventoried.

2.5 out of 2.5 points

2.5 out of 2.5 points

d. low levels of capital intensity.

Question 20

Regarding control charts, a type I error refers to concluding that the process is:

a. in control when it is not in control. b. incapable when it is capable.

c. out of control when it is in control. d. capable when it is not capable.

Question 21

Table 7.6

2.5 out of 2.5 points

0 out of 2.5 points

Burdell Industries makes four different models of computer printers: the E-

1000, the S-2000, the P-2000 and the N-1000. The E-1000 sells for $200 and

has $40 in parts and $40 in labor; the S-2000 sells for $150 and requires $30

in parts and $30 in labor; the P-2000 sells for $100 and has $20 in parts and

$20 in labor; and the N-1000 sells for $75 but requires only $10 of parts and

$10 of labor. Fixed overhead is estimated at $5,000 per week. The manufacture

of each printer requires four machines, Machines #1, 2, 3 and 4. Each of the

machines is available for 40 hours a week and there is no setup time required

when shifting from the production of one product to any other. The processing

requirements to make one unit of each product are shown in the table. Weekly

product demand for the next planning period has been forecasted as follows: 80

E-1000s; 65 S-2000s; 35 P-2000s; and 20 N-1000s.

Processing Time (Minutes Per Printer)

Model Machine

1 Machine 2 Machine 3 Machine 4

E-1000 (E) 10 15 15 5

S-2000 (S) 10 10 10 10

P-2000 (P) 5 10 15 10

N-1000 (N) 5 5 5 10

In the questions that follow, the traditional method refers to maximizing the contribution margin per unit for each product, and the bottleneck method refers

to maximizing the contribution margin per minute at the bottleneck for each product.

Use the information in Table 7.6. Using the bottleneck method, in what sequence should products be scheduled for production?

a. N, S, E, P b. N, E, P, S c. P, E, N, S d. E, S, P, N

Question 22

2.5 out of 2.5 points

A manufacturer that produces standard products in large volumes is likely to be using a(n):

a. make-to-stock strategy. b. make-to-order strategy.

c. assemble-to-order strategy. d. engineer-to-order strategy.

Question 23

Which one of the following statements about flexible automation is best?

a. Investment cost is lower when a transfer machine handles many operations.

2.5 out of 2.5 points

b. Chemical processing plants and oil refineries mainly utilize programmable automation. c. It is an automatic process that can be reprogrammed to handle various products.

d. It achieves top efficiency; accommodating new products is difficult and costly.

Question 24

Which statement regarding learning rates is best?

a.A more complicated process offers more room for improvement.

b.A simpler process has a more pronounced learning rate.

c. Typically, the effect of each capital addition on the learning curve is significant.

0 out of 2.5 points

d.Regardless of output volume, the estimate for the time required to produce the first unit is less important than the estimate of the

learning rate.

Question 25

You are given the following information about an activity A:

i) Normal time = 9 weeks ii) Crash time = 7 weeks iii) Normal cost = $20,000 iv) Crash cost = $30,000

What will it cost to complete activity A in 8 weeks?

a. Less than or equal to $24,000

b. Greater than $24,000 but less than or equal to $27,000 c. Greater than $27,000 but less than or equal to $30,000 d. Greater than $30,000

Question 26

Questions 27 & 28 apply to this information: Quill Manufacturing Business makes two models of marking pens. An unlabeled graph for this problem and the requirements for each lot of pens in the three manufacturing departments are given below. All three departments are necessary in the production of both types of pens. The profit for either kind of pen is $1000 per lot. An unlabeled graph for this problem is given below. The dotted line represents the objective function line.

Fliptop Model Tiptop Model Available production hrs.

Ink Assembly 3 4 36

Molding Time 5 4 40

Plastic 5 2 30

27. What is the optimal production quantity of the Fliptop model?

A. 5 lots

B. 4 lots

C. 2 lots

D. 7 lots

E. 6 lots

28. If all the constraint inequalities in the original problem were ≥, then the following is true:

A. The value of the objective function at the optimum solution is zero

B. There will be multiple optimal solutions

C. The problem will become unbounded

D. The problem has a unique solution

E. None of the above is true

29. Let M be the number of units to make and B be the number of units to buy of a certain product. If it costs $2 to make a unit and $3 to buy a unit and 4000 units are needed, the objective function of the LP model to minimize the cost of production would be,

A. Min 4000 (M + B)

B. Max 8000M + 12000B

C. Min 2M + 3B

D. Max 2M + 3B

E. Min 4000U -2M-3B

30. The Quiet Meadow Studio sells photographs and prints. It cost $20 to purchase each photograph and it takes 2 hours to frame it. It costs $25 to purchase each print and it takes 5 hours to frame it. The store has at most $400 to spend and at most 60 hours to frame.

It makes $30 profit on each photograph and $50 profit on each print. Determine the maximum profit.

A. 360

B. 600

C. 700

D. 740

E. 800

Questions 31 & 32 apply to this information: Quality Bike Maps has produced four map designs for the local area. A limited amount of time (in minutes) is allocated to the printing, cutting and folding of each map. Additionally, at least one thousand of map designs A, B, and C must be printed. The profit per map is $1 for A and B and $2 for C and D. The Excel output is provided below.

Max Profit = A + B + 2 C + 2 D

s.t.

A + 2 B + 3 C + 3 D < 15000 Print

2 A + 4 B + C + 3 D < 20000 Cut

3 A + 2 B + 5 C + 3 D < 20000 Fold

A > 1000 Print A

B > 1000 Print B

C > 1000 Print C

Microsoft Excel 14.0 Sensitivity Report

Objective Function Value $10,166.67

Variable Cells

Final Reduced Objective Allowable Allowable

Cell Name Value Cost Coefficient Increase Decrease

$B$18 Map A 1500 0 1 1 0.333333333

$C$18 Map B 1000 0 1 0.333333333 1E+30

$D$18 Map C 1000 0 2 0.333333333 1E+30

$E$18 Map D 2833.333333 0 2 1 0.5

Constraints

Final Shadow Constraint Allowable Allowable

Cell Name Value Price R.H. Side Increase Decrease

$B$24 Print 15000 0.5 15000 1000 5666.666667

$B$25 Cut 16500 0 20000 1E+30 3500

$B$26 Fold 20000 0.166666667 20000 7000 1000

$B$27 Print A 1500 0 1000 500 1E+30

$B$28 Print B 1000 -0.33333333 1000 1750 1000

$B$29 Print C 1000 -0.33333333 1000 500 1000

31. Answer the following question using the Excel output above. Which constraint(s) are binding?

A. Print and Fold

B. Cut and Print A

C. Print B and Print C

D. Print and Cut

E. Print, Fold, Print B and Print C

32. Answer the following question using the Excel output above. Keeping within the confines of the problem, the profit on Map A has increased by one dollar. Determine the new objective function value.

A. 1,500

B. 11,166.67

C. 11,500.67

D. 11,666.67

E. 12,566.67

33. Quentin Magic Brown manufactures sports shoes and wants to maximize the company’s profits. The company makes two types of sport shoe, Airwalkers and Bouncy Basketball shoes. The company earns $10 profit on each pair of Airwalkers and $18 profit on each pair of Bouncy Basketball shoes.

The manufacturing process includes cutting the materials on a machine and having workers assemble the pieces. Each pair of Airwalkers requires 3 minutes of cutting time and the Bouncy Basketball shoes require 2 minutes. The machines that cut the material can run at most 1200 minutes a week.

Each worker takes 7 hours to assemble a pair of Airwalkers and 8 hours to assemble a pair of Bouncy Basketball shoes; the maximum number of hours available is 3500 per week.

Determine the maximum profit for this problem?

A. $3200

B. $4000

C. $4280

D. $6295

E. $7875

Questions 34-37 apply to the Excel output for the Quantum Mo-Botics model is below. The company makes three types of machines and has limitations with regards to the amount of skilled and unskilled labor hours available and time on the assembly line.

MAX Profit = 800SemiAuto+1000Robotic + 500Manual

s.t.

30SemiAuto + 100Robotic + 45Manual < 4500 Skilled Labor

100SemiAuto + 70Robotic + 90Manual < 9000 Unskilled Labor

15SemiAuto + 20Robotic + 10Manual < 2000 Assembly Line

Microsoft Excel 14.0 Sensitivity Report

Objective Function Value $ 82,025.32

Variable Cells

Final Reduced Objective Allowable Allowable

Cell Name Value Cost Coefficient Increase Decrease

$B$18 SemiAuto 74.05063291 0 800 628.5714286 432.4786325

$C$18 Robotic 22.78481013 0 1000 1666.666667 440

$D$18 Manual 0 -320.253164 500 320.2531646 1E+30

Constraints

Final Shadow Constraint Allowable Allowable

Cell Name Value Price R.H. Side Increase Decrease

$B$24 Skilled labor 4500 5.569620253 4500 3605.263158 1800

$B$25 Unskilled labor 9000 6.329113924 9000 3805.555556 5850

$B$26 Assembly line 1566.455696 0 2000 1E+30 433.5443038

34. Answer the following question using the Excel output above, determine the new objective function value if the profit on the second variable, Robotic, increases by $1000?

A. $22,785.00

B. $19,125.64

C. $33,800.00

D. $102,805.32

E. $104,810.32

35. Answer the following question using the Excel output above. Keeping within the confines of the problem, you are required to hire a full time (40 hours) person who is qualified to work in any department. Select the constraint where you will gain the most profit and determine the additional profit to be gained?

A. $253.16

B. $222.80

C. $341.00

D. $129.50

E. $119.50

36. Answer the following question using the Excel output above. Keeping within the confines of the problem, how many more hours of skilled workers could you add to the department?

A. 2875.33

B. 1280.56

C. 1550.56

D. 3805.56

E. 3605.26

37. Using the Excel output above, how much is each additional unit of unskilled labor worth?

A. $74.500

B. $22.790

C. $5.570

D. $6.329

E. $3.250

38. An ice cream plant make’s Chocolate and Strawberry ice cream.

There is $40 profit for a case of Chocolate and $32 for a case of Strawberry and has the following constraints:

32C + 8S < 4,800 Flavoring

28C + 32S < 14,000 Coloring

a. What is the optimal solution?

b. Now add a constraint: demand for Strawberry is always less than 200 cases and determine the optimal solution.

c. Add another constraint: demand for Chocolate is always less than 400 cases and determine the optimal solution.

Solution-

38a ( 52,392) $14,624

38b (100,200) $10,400

38c redundant constraint; no change

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