The Flamingo Restaurant Recommendation
Student’s Name
Institutional Affiliation
The Flamingo Restaurant Recommendation
Executive summary
The Flamingo Grill is an upscale restaurant located in St. Petersburg, Florida. The Flamingo management team seeks an efficient advertising plan for coming season with considerations to use three media; television, radio and internet. However, the team faces the challenge of distributing the available budget of $ 279,000 among the three media. To solve the challenge, Flamingo’s management team hired Haskell and Johnson an advertising firm to seek a recommendation on how to distribute the adverting budget with a consideration to maximize total exposure rate, and new customers reached.
Introduction
Allocating limited resources among many alternative uses in the management of businesses and companies, has necessitated the incorporation of mathematical techniques such as linear programming. Linear programming (LP) is a powerful mathematical technique used to allocate limited resources among many alternative uses to find optimal benefits (Sakawa et al., 2013). Haskell and Johnson consider employing linear programming in management of the Flamingo restaurant advertising budget to maximize the total exposure rate. The maximizing of total exposure rate will ensure that the number of new customers reached increases. Haskell and Johnson consider two options that will ensure that the number of new customers increases. The first option is to use the exposures’ effectiveness rating per ad and estimate the number of potential new customers reached. The second option is to increase the advertising budget of $ 279,000 by an additional budget of $ 10,000. Therefore, Haskell and Johnson use a linear programming model and sensitivity analysis to conclude. Importantly, the assumptions of proportionality and additive hold but divisibility do not hold in regards decision variable. We cannot have a fraction of advertisement. Below is the manager report.
Managerial report
| The industry | Changes for planning purposes | |||||
| Advertising Media |
Exposure Rating per Ad |
New Customers per Ad |
Advertising Media |
Exposure Rating per Ad |
New Customers per Ad |
Cost per Ad |
| Television | 90 | 4000 | Television | 55 | 1500 | $10,000 |
| Radio | 25 | 2000 | Radio | 20 | 1200 | $ 3,000 |
| Internet | 10 | 1000 | internet | 5 | 800 | $1,000 |
The above table presents the industry’s exposure rating per Ad, an estimate of the new customer reached per Ad, and he cost per Ad. Also, the table presents Flamingo’s recommended changes in exposure rate per Ad, an estimate of new customers reach per Ad and the cost per Ad for planning purposes.
The exposure rating and new customers reached are expected to decline after 10 television Ads, 15 radio Ads, and 20 internet Ads reducing the optimal benefits. The total exposure rate must ensure that new customers reached exceed 100,000
Decision Variables:
Tv1= number of television ads with a rating of 90 and 4000 new customers
Tv2= 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
In1= number of internet ads with a rating of 10 and 1000 new customers
In2= number of internet ads with a rating of 5 and 800 new customers
Advertising Budget = $279,000; Television Ads >= $140,000, Radio Ads <= $99,000 and Internet ads >= $30,000
Objective Function and Constraints
The number of new reached customers is affected by the total exposure rate; therefore, we need to formulate an objective function aimed at maximizing the total exposure rate.
Maximize (Total exposure rate)= 90Tv1+55Tc2+25R1+20R2+10In1+5In2
S.t. ;
10,000Tv1 + 10,000Tv2 + 3,000R1 + 3,000R2 + 1,000 In1 + 1,000 In2 < = 279,000 (Total budget )
4,000Tv1 + 1,500Tv2 + 2,000R1 + 1,200R2 + 1,000 In1 + 800 In 2 >= 100,000 (New Customers)
10,000Tv1 + 10,000Tv2 >= 140,000 (TV budget
3,000R1+3,000R2 =< 99,000 (Radio budget)
1,000 In1+1,000 1n 2 >= 30,000 (Internet budget)
-2Tv1 + -2Tv2 + R1 + R2 >= 0 (Radio advertisement Ad)
Tv1< =10 (television first 10 Ads)
R1< = 15 (radio first 15 Ads)
In1< =2 (Internet first 20 ads)
Tv1, Tv2, R1, R2, In1, In2>0 (Non-negative)
Budget scheduling
The use of excel linear programming model to evaluate the formulated objective function provided the below optimal solutions.
Total television Ads = Tv1+Tv2 = (10+5 )=15
Total radio Ads = R1+R2= (15+18) =33
Total internet Ads = In1+In2= (20+10)= 30
However, the cost per ad for Television, radio and internet are $ 10,000, $3,000 and $ 1000 respectively.
| Advertising media | Budget allocation |
| Television Ads | (15* $10,000) = $ 150,000 |
| Radio Ads | (33*$ 3,000)= $ 99,000 |
| Internet Ads | (30*$1,000) = $ 30,000 |
| Total budget = $ 279,000 |
The budget is forecasted to reach a total of 127,100 new customers with the effectiveness of 2,160 total exposure rates.
Additional budget allocation
The second option of increasing the number of new customers by use of additional budget requires a sensitivity analysis. In the sensitivity analysis, the shadow price for the budget 0.0055. The shadow price is positive. Therefore an additional budget will increase the total exposure rate. The additional budget is $ 10,000, therefore change in exposure will be (0.0055*10,000) =55 exposure rates. The total exposure rate will increment by 55 exposure rate to a total exposure rate of 2,215.
Conclusion
The employment of linear programming and sensitivity To maximize the total exposure rates and new customers reached by Haskell and Johnson advertising firms provides two option plans for the Flamingo Grill management to use. Flamingo Grill can use15 television ads, 33 radio ads, and 30 internet ads at a budget of $ 279,000. However, through the use of sensitivity analysis, an additional budget will also lead to an increase in the total exposure rate.
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Reference
Sakawa, M., Yano, H., Nishizaki, I. and Nishizaki, I., 2013. Linear and multiobjective programming with fuzzy stochastic extensions. New York, NY, USA:: Springer US.