##### 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

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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

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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

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Paper#9210793 | Written in 27-Jul-2016

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