Case Problem 2 Schneidar\'s Sweot Shop 205 Managerial Report Develop a model tha
ID: 2807646 • Letter: C
Question
Case Problem 2 Schneidar's Sweot Shop 205 Managerial Report Develop a model that can be used to determine the advertising budget allocation for the Flamingo Grill. Include a discussion of the following in your report. A schedule showing the recommended number of television, radio, and newspaper advertisements and the budget allocation for each medium. Show the total exposure and indicate the total number of potential new customers reached. 1. 2. How would the total exposure change if an additional $10,000 were added to the advertising budget? 3. A discussion of the ranges for the objective function coefficients. What do the ranges indicate about how sensitive the recommended solution is to HJ's exposure rating coefficients? 4. After revicwing HJ's recommendation, the Flamingo's management team asked how the recommendation would change if the objective of the advertising cam- paign was to maximize the number of potential new customers reached. Develop the media schedule under this objective. 5. Compare the recommendations from parts I and 4. What is your recommendation for the Flamingo Grill's advertising campaign?Explanation / Answer
1.Advertising Schedule:
Media
Number of Ads
Budget
Television
15
$150,000
Radio
33
$99,000
Newspaper
30
$30,000
Total
78
$279,000
Total Exposure: 2160
Total New Customers Reached: 127,100
Explanation:
Given:
Initial Exposure
After Initial Exposure
Advertising
Media
Exposure
Rating per Ad
New Customers
per Ad
Cost
per Ad
Advertising
Media
Exposure
Rating per Ad
New Customers
per Ad
Cost
per Ad
Television
90
4000
$10,000
Television
55
1500
$10,000
Radio
25
2000
$3,000
Radio
20
1200
$3,000
Newspaper
10
1000
$1,000
Newspaper
5
800
$1,000
Exposure rating and new customers reached decreases after 10 TV ads, 15 radio ads, and 20 newspaper ads.
New Customers Reached > 100,000
Advertising Budget = $279,000;(Television ads > $140,000; Radio ads < $99,000; Newspaper ads > $30,000)
Decision Variables:
T1= number of television ads with a rating of 90 and 4000 new customers
T2= number of television ads with a rating of 55 and 1500 new customers
R1= number of radio ads with a rating of 25 and 2000 new customers
R2= number of radio ads with a rating of 20 and 1200 new customers
N1= number of newspaper ads with a rating of 10 and 1000 new customers
N2= number of newspaper ads with a rating of 5 and 800 new customers
Objective Function and Constraints
Max
90T1 + 55T2 + 25R1 + 20R2 + 10N1 + 5N2
s.t.
T1 < 10
R1 < 15
N1 < 20
10,000T1 + 10,000T2 + 3,000R1 + 3,000R2 + 1,000N1 + 1,000N2 < 279,000
4,000T1 + 1,500T2 + 2,000R1 + 1,200R2 + 1,000N1 + 800N2 > 100,000
-2T1 + -2T2 + R1 + R2 > 0
T1 + T2 < 20
10,000T1 + 10,000T2 > 140,000
3,000R1 + 3,000R2 < 99,000
1,000N1 + 1,000N2 > 30,000
T1, T2, R1, R2, N1, N2 > 0
Optimal Solution: Budget Allocation:
T1 = 10, T2 = 5; 10 + 5 = 15 Television ads 15 * 10,000 = $150,000
R1 = 15, R2 = 18; 15 + 18 = 33 Radio ads 33 * 3,000 = $99,000
N1 = 20, N2 = 10; 20 + 10 = 30 Newspaper ads 30 * 1,000 = $30,000
2. If $10,000 is added, then the budget will change by = 10,000 *shadow price
=10,000 * 0.0055 = 55 points
Here, the shadow price for the budget constraint is 0.0055.
Thus, with this additional 10,000, the total exposure will increase by 55 points.
3. Here, in the given problem there is a huge difference in the new customers reached and number of ads suggested in the part 1 and 4 schedules. Thus, the solution is not very sensitive to the exposure rating coefficients.
4.Advertising Schedule:
Media
Number of Ads
Budget
Television
14
$140,000
Radio
28
$84,000
Newspaper
55
$55,000
Total
97
$279,000
Total Exposure= 90(10) + 55(4) + 25(15) + 20(13) + 10(20) + 5(35) = 2130
Total New Customers Reached: 139,600
5.I would recommend using the advertising schedule from part 4 instead of the original schedule because more new customers would be reached and the exposure would only decrease by 30 points.
Media
Number of Ads
Budget
Television
15
$150,000
Radio
33
$99,000
Newspaper
30
$30,000
Total
78
$279,000