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PRODUCTION & OPERATIONS MANAGEMENT FINAL EXAMINATION --(Answered)

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PRODUCTION & OPERATIONS MANAGEMENT

 

FINAL EXAMINATION ? SPRING 2016

 

NAME_______________________________________

 


 

(1) REGRESSION ANALYSIS (applications)

 

A business person in Georgia State is trying to estimate the relationship

 

between the average weekly income in a county and the weekly expenditure

 

on a certain staple Z. Data is collected in 6 counties and below is the

 

tabulation:

 

Average Income / Week

 


 

Average Expenditure on Z

 


 

$200

 

$250

 

$300

 

$350

 

$400

 

$500

 


 

103.00

 

91.00

 

82.00

 

65.00

 

51.00

 

23.00

 


 

A simple linear regression of a model EXPENDITURE = b + b INCOME

 

0

 


 

1

 


 

Was run and the computer output is shown below:

 

INCOME & EXPENDITURE ON STAPLE Z

 

REGRESSION FUNCTION & ANOVA FOR EXPEND[Z]

 

EXPEND[Z] = 159.0714 - 0.269714 INCOME

 

R-Squared

 

Adjusted R-Squared

 

Standard error of estimate

 

Number of cases used

 


 

= 0.994999

 

= 0.993749

 

= 2.309143

 

=6

 

Analysis of Variance

 


 

Source

 

SS

 

Regression 4243.50500

 

Residual

 

21.32857

 

Total

 

4264.83300

 


 

df

 

MS

 

1 4243.50500

 

4

 

5.33214

 

5

 


 

1

 


 

F Value

 

795.83480

 


 

p-value

 

Sig Prob

 

0.000009

 


 

INCOME & EXPENDITURE ON STAPLE Z

 

REGRESSION COEFFICIENTS FOR EXPEND[Z]

 

Variable

 

Constant

 

INCOME

 


 

Coefficient Std Error

 

159.07140

 

3.32342

 

-0.26971

 

0.00956

 


 

Standard error of estimate

 

Durbin-Watson statistic

 


 

Two-Sided

 

t Value

 

47.86370

 

-28.21054

 


 

p-value

 

Sig Prob

 

0.000001

 

0.000009 *

 


 

= 2.309143

 

= 1.687953

 


 

QUESTIONS

 

(a) What is the estimated equation for the model:

 

EXPENDITURE = b + b INCOME

 

0

 


 

1

 


 

ANSWER

 


 

(b) What kind of relationship exists between average income and

 

average expenditure on staple Z? Does this relationship make sense

 

to you? Why or why not?

 

ANSWER

 


 

(c) What can you say about staple Z? (what sort of good is staple Z?)

 

ANSWER

 


 

(d) Interpret the values of the b-coefficients (intercept and slope) in the

 

estimated regression.

 

b =?

 

0

 


 

2

 


 

b =?

 

1

 


 

What are your interpretations of these values?

 


 

(e) At a level of significance ? = 0.01, test for the validity of the

 

relationship. What is your conclusion?

 

EXPENDITURE = b + b INCOME

 

0

 


 

1

 


 

H :b =0

 

0

 


 

1

 


 

H :b ?0

 

A

 


 

1

 


 

What is your conclusion? Is the regression statistically significant? Why?

 


 

(f) Forecast the expected expenditure on staple Z for a household with

 

average weekly income of (i) $100, (ii) $600. To come up with your

 

forecasts what assumption(s) did you make?

 


 

3

 


 

(2) REGRESSION ANALYSIS

 

A business person in Georgia State is trying to estimate the relationship

 

between the average weekly income in a county and the weekly expenditure

 

on a certain staple X. Data is collected in 6 counties and below is the

 

tabulation:

 

Average Income / Week

 

$150

 

$200

 

$250

 

$300

 

$400

 

$500

 


 

Average Expenditure on X

 

$33

 

$39

 

$47.50

 

$55

 

$65.50

 

$72.50

 


 

A simple linear regression of a model EXPENDITURE = b + b INCOME

 

0

 


 

1

 


 

Was run and the computer output is shown below:

 


 

INCOME & EXPENTITURE ON STAPLE X

 

REGRESSION FUNCTION & ANOVA FOR EXPEND[X]

 

EXPEND[X] = 17.40686 + 0.115588 INCOME

 

R-Squared

 

= 0.977573

 

Adjusted R-Squared

 

= 0.971966

 

Standard error of estimate = 2.552152

 

Number of cases used

 

=6

 

Analysis of Variance

 


 

p-value

 

Source

 

SS

 

Regression 1135.65400

 

Residual

 

26.05392

 

Total

 

1161.70800

 


 

df

 

MS

 

1 1135.65400

 

4

 

6.51348

 

5

 


 

F Value

 

174.35450

 


 

Sig Prob

 

0.000190

 


 

INCOME & EXPENTITURE ON STAPLE X

 

4

 


 

REGRESSION COEFFICIENTS FOR EXPEND[X]

 

Variable

 

Constant

 

INCOME

 


 

Coefficient

 

17.40686

 

0.11559

 


 

Std Error

 

2.82528

 

0.00875

 


 

Two-Sided

 

t Value

 

6.16111

 

13.20434

 


 

p-value

 

Sig Prob

 

0.003522

 

0.000190 *

 


 

Standard error of estimate = 2.552152

 

Durbin-Watson statistic = 1.240299

 


 

QUESTIONS

 

(a) What is the estimated equation for the model:

 

EXPENDITURE = b + b INCOME

 

0

 


 

1

 


 

ANSWER

 


 

(b) What kind of relationship exists between average income and average

 

expenditure on staple X? Does this relationship make sense to you?

 

Why or why not?

 

ANSWER

 


 

(c) What can you say about staple X? (What sort of good is staple X?)

 

ANSWER

 


 

5

 


 

(d) Interpret the values of the b-coefficients (intercept and slope) in the

 

estimated regression.

 

b =?

 

0

 


 

b =?

 

1

 


 

What are your interpretations of these values?

 


 

(e) At a level of significance ? = 0.01, test for the validity of the

 

relationship. What is your conclusion?

 

EXPENDITURE = b + b INCOME

 

0

 


 

1

 


 

H : b = 0 null hypothesis

 

0

 


 

1

 


 

H : b ? 0 alternative hypothesis

 

A

 


 

1

 


 

What is your conclusion? Is the regression statistically significant? Why?

 

ANSWER

 


 

(f) Forecast the expected expenditure on staple Z for a household with

 

average weekly income of (i) $100, (ii) $600. To come up with your

 

forecasts what assumption(s) did you make?

 


 

6

 


 

PROJECT MANAGEMENT & CONTROL

 

A consulting firm is working on a project and has sorted out the required

 

activities as well as activities order as follows:

 

ACTIVITY

 

A

 

B

 

C

 

D

 

E

 

F

 

G

 

H

 


 

TIME WKS

 

3

 

4

 

2

 

6

 

7

 

4

 

4

 

2

 


 

IMMEDIATE PRED

 

A

 

A, B

 

C, D

 

D

 

E, F

 

F, G

 


 

The network has been drawn as illustrated below.

 

C

 

A

 


 

E

 

G

 


 

Start

 


 

D

 


 

H

 


 

B

 


 

F

 


 

USE THE COMPUTATION TABLE BELOW TO IDENTIFY (a) SCHEDULED

 

TIMES, (2) CRITICAL ACTIVITIES, and (C) Non-CRITICAL ACTIVITIES AND

 

THEIR SLACK TIMES.

 


 

7

 


 

Finis

 


 

Computational Table

 

ACTIVITY

 

A [3]

 

B [4]

 

C [2]

 

D [6]

 

E [7]

 

F [4]

 

G [4]

 

H [2]

 


 

ES

 


 

EF

 


 

LS

 


 

LF

 


 

SLACK

 

LS - ES

 


 

CRITICAL?

 


 

ANSWERS: (a) CRITICAL ACTIVITIES ARE:

 

(b) THE CRITICAL PATH IS:

 

(c) NON-CRITICAL ACTIVITIES AND THEIR SLACK TIMES ARE:

 

WAITING LINES

 

1. A homemade-ice cream shop has noticed that, often, potential

 

customers will stop outside the store, assess the length of the waiting

 

line, and then decide whether to go in or just pass by. This kind of

 

behavior is known as reneging. True / False

 

2. The owner of a desktop publishing company has 20 loyal clients who

 

periodically require her services. The owner has a finite customer

 

population. True / False

 

3. A PC accessory discount store often has customers who leave the

 

checkout line before being served because of excessive waiting times.

 

This type of customer behavior in waiting lines is known as balking.

 

True / False

 

4. A Laundromat where there are 10 washing machines and 10 drying

 

machines is an example of multiple-channel, multiple- phase. True /

 

False

 


 

8

 


 

5. A drive-through system of a fast-food restaurant where customers

 

form a single queue and the first server takes orders, then the second

 

server takes the payments for the food, then the third server hands

 

over the ordered food is an example of multiple-channel, single

 

phase. True / False

 


 

ECONOMIC ORDER QUANTITY MODEL (INVENTORY MGMT &

 

CONTROL): BASIC EOQ MODEL IS Order Quantity Q =

 

2 DS / H

 


 

(1) Items purchased from a vender cost $20 each, and the forecast for the

 

next year?s demand is 1,000 units. The cost of placing an order is

 

estimated to be $5 every time an order is placed. Storage costs are $4

 

per unit per year. What quantity should be ordered to minimize

 

inventory related costs?

 


 

(2)

 


 

Ray?s Satellite Emporium wishes to determine the best order size of

 

their best selling satellite dish (model TS111). Ray has estimated the

 

annual demand for this model at 1,000 units. His cost to carry one

 

unit is $100 per year per unit, and he has estimated that each order

 

costs $25 to place. Based on the EOQ model, how many units should

 

Ray order each time he places an order?

 


 

9

 


 

THE NEWSBOY PROBLEM ? INVENTORY MODELS FOR

 

PERISHABLES ( C = cost of shortage of 1 unit, C = cost of excess of 1

 

s

 


 

E

 


 

unit)

 

SERVICE LEVEL =

 


 

C

 

S

 


 

C

 


 

+

 


 

C

 


 

S

 


 

E

 


 

(3) Sally?s Silk Screening produces special T-shirts that are primarily sold

 

on the Halloween day. She must decide how many to produce for the

 

coming Halloween. During the event itself, which lasts one day, Sally

 

can sell a T-shirt for $20 a-piece. However, when the event ends, any

 

unsold T-shirts are sold for $4 a-piece. It costs Sally $8 to make a

 

specialty T-shirt. Using Sally?s estimated distribution of demand, how

 

many T-shirts should she produce for the coming event?

 

DEMAND

 

300

 

400

 

500

 

600

 

700

 

800

 


 

Probability

 

.05

 

.10

 

.40

 

.30

 

.10

 

.05

 


 

COMPUTE COMULATIVE PROBABILITY

 


 

Hint: What is the optimal service level? What is the cumulative probability

 

distribution?

 


 

(4) The Lake Nocee Department Store has an opportunity to purchase a

 

special shipment of X-mas tableware at $28 a set. These sets of

 

tableware are to be sold for $35 as a special promotion during the

 

store?s 40th anniversary sale. Nocee must purchase the items in units

 

of a dozen sets. Tableware is not part of the store?s normal product

 

10

 


 

lines, so if items are not sold during the X-mas cum 40 th anniversary,

 

they will be sold in the Bargain Basement for $22.20 per set. A sales

 

consultant has estimated the following distribution of demand.

 

Demand (Dozens)

 

4 or less

 

5

 

6

 

7

 

8

 

9

 

10

 

11

 

12

 


 

Probability

 

0

 

0.10

 

0.15

 

0.25

 

0.20

 

0.15

 

0.10

 

0.05

 

0

 


 

Determine the optimal order quantity for Nocee regarding this item.

 


 

Aggregate Planning

 

Problem # 1

 

Pomegranate Juice, Inc., produces bottled pomegranate juice.

 

A

 

planner has developed an aggregate forecast for demand (in cases) for

 

the next six months as:

 

Month

 

Forecast

 


 

1

 

400

 


 

2

 

480

 


 

3

 

560

 


 

4

 

720

 

11

 


 

5

 

640

 


 

6

 

500

 


 

Total

 


 

Costs:

 

Output

 

Regular time

 

Regular production capacity

 

Overtime production cost

 

Subcontracting cost

 

Inventory Holding cost

 

Beginning inventory

 


 

=

 

=

 

=

 

=

 

=

 

=0

 


 

$10 per case

 

500 cases per month

 

$16 per case

 

$20 per case

 

$1 per/case/month on avg

 


 

Develop an aggregate production plan using the following guideline

 

and compute the total cost for the plan

 

(a) Policy ? level production plan, supplemented by

 

inventory and overtime as needed

 

USE THE COMPUTATIONAL TABLE BELOW

 


 

COMPUTATION AID

 

Period

 

Forecast

 

Output:

 

Regular

 

Overtime

 

Subcontract

 

Output - Forecast

 

Inventory

 

Beginning

 

Ending

 

Average

 

Backlog

 

Costs:

 

Output

 

Regular

 

Overtime

 

Subcontract

 

Inventory

 

Back orders

 

TOTAL

 


 

1

 

400

 


 

2

 

480

 


 

3

 

560

 


 

4

 

720

 


 

5

 

640

 


 

6

 

500

 


 

Total

 

3300

 


 

500

 

-----

 


 

500

 

-----

 


 

500

 

-----

 


 

500

 

-----

 


 

500

 

-----

 


 

500

 

-----

 


 

3000

 

---------

 


 

-----

 


 

-----

 


 

-----

 


 

-----

 


 

-----

 


 

-----

 


 

-------------

 


 

12

 


 

13

 


 

 

Paper#9210793 | Written in 27-Jul-2016

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