Assignment
Problem 1 - 3
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:
Max 3x_1+2x_2
subject to
2x_1+x_2≥6
x_1≥2
x_1,x_2≥0
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.
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YR
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Unemployment Rate (%)
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1
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5.1
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2
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5.6
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3
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5.3
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4
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5.5
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5
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5.3
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6
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5.2
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7
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6.3
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8
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6.4
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9
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5.8
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10
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Forecast =
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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:
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Territory
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Share
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Knowledge
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Professionalism
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Trust
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1
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23
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7
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4
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6
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2
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15
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6
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5
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6
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3
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13.75
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6
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6
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8
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4
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5
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6
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5
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4
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S
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30
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7
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7
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9
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6
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6.2
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5
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3
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3
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7
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28.4
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7
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7
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9
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8
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21.25
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4
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8
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8
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9
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16.25
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7
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3
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5
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10
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11.25
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8
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6
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4
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11
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15
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5
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6
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7
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12
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28
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9
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6
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8
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SUMMARY OUTPUT
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Regression Statistics
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Multiple R
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0.858639
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R Square
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0.737261
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Adjusted R Square
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0.718036
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Standard Error
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3.661626
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Observations
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45
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ANOVA
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df
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SS
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MS
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F
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Regression
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3
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1542.51416
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514.1714
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38.349511
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Residual
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41
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549.7078397
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13.40751
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Total
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44
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2092.222
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Coefficients
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Standard Error
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t Stat
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P-value
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Intercept
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-1.87568
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3.003934553
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-0.62441
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0.53581948
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Knowledge
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0.812617
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0.371804742
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2.185601
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0.03461216
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Professionalism
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-0.23212
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0.361683503
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-0.64177
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0.52459135
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Trust
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2.535171
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0.27729141
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9.142622
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1.9036E-11
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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?
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Share
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Knowledge
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Professionalism
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Trust
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Territory 100
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7
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9
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6
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Territory 101
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6
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5
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9
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Territory 102
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8
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9
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8
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Territory 103
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8
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2
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9
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(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 itemssold 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
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# of calls
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Items Sold
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17
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2,130
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11
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1,587
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7
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942
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11
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1,512
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18
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1,857
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13
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1,284
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12
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951
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5
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615
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10
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1,404
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12
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1,635
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13
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1,821
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18
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2,082
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14) 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: 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.
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Task
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Task time per worker
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Number of workers
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1
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2 minutes
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1
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2
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6 minutes
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1
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3
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14 minutes
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2
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4
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4 minutes
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1
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5
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15 minutes
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3
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a. What is the capacity (hourly) of the process as a whole?
b. What is the bottleneck of the process?
c. What is the throughput time (assuming no wait time)?
d. Where would you expect customers to wait?
Problem 17: 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).
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Month
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Jan
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Feb
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Mar
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Apr
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May
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Jun
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July
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Aug
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Sept
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Oct
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Nov
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Dec
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Jan
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Format your assignment according to the following formatting requirements:
1. The answer should be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides.
2. The response also includes a cover page containing the title of the assignment, the student's name, the course title, and the date. The cover page is not included in the required page length.
3. Also include a reference page. The Citations and references should follow APA format. The reference page is not included in the required page length.