Business Analytics Homework

A candidate for mayor in Newtown, PA has allocated $40,000 for last-minute advertising in the days preceding the election. Two types of ads will be used: newspaper and television. Each newspaper ad costs $300 and reaches an estimated 4,000 people. Each television ad costs $500 and reaches an estimated 7,000 people. In planning the advertising campaign, the campaign manager would like to reach as many people as possible, but she has stipulated that at least 10 ads of each type must be used. Also, the number of newspaper ads must be at least 10% more than the number of television ads.

Let N = # of Newspaper ads; T = # of TV ads

1) How would you write the constraint for requiring 10% more newspaper ads than TV ads?

a) N 1.1

b) N + T 1.1

c) N – 0.1T 0

d) N – 1.1T 0

e) None of the above

2) What is the budget constraint for this problem?

a) 4,000N + 7,000T 40,000

b) 500N + 300T 40,000

c) 500N + 300T 40,000

d) 300N + 500T 40,000

e) None of the above

3) What is the objective function for this problem?

a) Minimize Cost = 300N + 500T

b) Maximize Spending = 40,000(N + T)

c) Maximize Profit = 300N + 500T

d) Maximize Reach = 4,000N + 7,000T

e) None of the above

Problem 4: In linear Programming, a constraint that does not affect the feasible region is

(a) non-negativity constraint.

(b) redundant constraint.

(c) standard constraint.

(d) slack constraint.

(e) none of the above

Problem 5: Forecast errors

(a) are the difference in successive values of a time series

(b) are the differences between actual and forecast values

(c) should all be nonnegative

(d) should be summed to judge the goodness of a forecasting model

(e) none of the above

Problem 6: Consider the LP below:

Determine if the LP:

(a) Has no feasible solution

(b) Is unbounded

(c) Has redundant constraints

(d) None of the above

Problem 7-8: The following table shows the unemployment rate in Pennsylvania for the last nine years.

7) Using 3 year Moving Average method, forecast the unemployment rate for the 10th year.

(a) 5.82

(b) 6.17

(c) 6.35

(d) 6.08

(e) 5.99

8) What is the Mean Square Error (MSE) for this forecasting approach?

(a) 0.29

(b) 1.76

(c) 0.07

(d) 0.64

(e) None of the above

Problem 9-11

The top management of a large pharmaceutical company located in NJ wants to forecast product share of new territories based on knowledge, professionalism, and trust-ability of a sales representative. Following is the sampled data, and subsequent output from multiple regressions:

9) You are to place four different sales representatives with different sales attributes (shown below) to the following new territories. Which territory has the highest share forecast?

(a) Territory 100

(b) Territory 101

(c) Territory 102

(d) Territory 103

10) Among the independent variables listed below, which one is the most significant to the product share?

(a) Knowledge

(b) Professionalism

(c) Trust

(d) Territory

11) What is the territory’s share forecast of a sales rep with knowledge of 6, professionalism of 7, and trust level of 8?

(a) 21.7

(b) 23.5

(c) 19.8

(d) 24.2

(e) None of the above

Problem 12: What does the state of nature refer to in a decision problem?

(a) Chance events

(b) Alternates

(c) Outcomes

(d) Probabilities

Problem 13-14: The top management of a large pharmaceutical company located in NJ wants to forecast items sold for each of their new territories based on the number of sales calls made by their sales agents. Following is a portion of the complete monthly data. Based on the complete data, the intercept is 227.68 and slope is 103.34 for the regression

13) What is the minimum # of calls needed to sell 2,600 items?

(a) 23 calls

(b) 24 calls

(c) 25 calls

(e) None of the above

14) If each sales call costs the company $315, and the revenue generated from an item sold is $3, which of the following strategy has the highest profit?

(a) 12 calls

(b) 14 calls

(c) 11 calls

(d) 17 calls

(e) None of the above

Problem 15: Here is a Linear Programming formulation where x, y are the decision variables:

Maximize Z = 4x + 3y;

Subject to:

I. x > 0

II. y > 0

III. x+2y<250

IV. 4x+8y<2000

Is there a redundant constraint in this problem?

(a) Constraints I, II

(b) Constraint III

(c) Constraint IV

(d) There are no redundant constraints.

Problem 16-19: A service has five tasks, performed in sequence. In the instance when there is more than one worker assigned to a task, each worker performs the entire task and they both can be working on different “items” at the same time.

1. What is the capacity (hourly) of the process as a whole?

1. What is the bottleneck of the process?

1. What is the throughput time (assuming no wait time)?

1. Where would you expect customers to wait?

Problem 20: Show how you will code the dummy variables in this model, in other words fill in 13 rows with your dummy variables in the table below. (the first column, Month, tells you what month it is).

TerritoryShareKnowledgeProfessionalismTrust

123746

215656

313.75668

45654

530779

66.2533

728.4779

821.25488

916.25735

1011.25864

1115567

1228968

SUMMARY OUTPUT

Regression Statistics

Multiple R0.858639

R Square0.737261

Adjusted R Square0.718036

Standard Error3.661626

Observations45

ANOVA

dfSSMSF

Regression31542.51416514.171438.349511

Residual41549.707839713.40751

Total442092.222

CoefficientsStandard Errort StatP-value

Intercept-1.875683.003934553-0.624410.53581948

Knowledge0.8126170.3718047422.1856010.03461216

Professionalism-0.232120.361683503-0.641770.52459135

Trust2.5351710.277291419.1426221.9036E-11

ShareKnowledgeProfessionalismTrust

Territory 100796

Territory 101659

Territory 102898

Territory 103829

# of calls

Items

sold

172,130

111,587

7942

111,512

181,857

131,284

12951

5615

101,404

121,635

131,821

182,082