Chinese to English translation

The parametric analysis, to find hope in what level of exposure will increase. ) Abstract:Super Grain Corporation's vice president, Claire Syverson, to a certain budget, will be the company's new breakfast cereal ─ Crunchy Start ─ sell to customers, and how the smallest budget, maximum exposure is the The main core of the case.Case Background:After studying the survey, breakfast cereals market in 2005, the estimated value of 8.9 billion, and from 2000 to 2005, its annual growth rate of at least 1% or more. And Claire Syverson order to the company's new breakfast into this market, selling to customers, and target customer set in the pediatric population, so the main advertising media in children's viewing of TV programs, or is the food and family-oriented magazines, and major newspaper Sunday supplement, the details are as follows:Medium 1: Television commercials on Saturday morning programs for children.Medium 2: Advertisements in food and family-oriented magazines.Medium 3: Advertisements in Sunday supplements of major newspapers.At present, Super Grain Corporation's total advertising budget of $ 4,000,000, the total advertising budget plan is $ 1,000,000, the remainder by the advertising design company, Giacomi & Jackowitz, information provided as follows:

Table 1: Cost and exposure data

Costs

Cost CategoryEach TV

CommercialEach

Magazine AdEach

Sunday AdAdvertising costs $300,000 $150,000 $100,000Planning costs $ 90,000 $ 30,000 $ 40,000Expected numberof exposures

1,300,000 600,000 500,000

(Of which, TV Commercial's greatest resource is 5 units.)

In principle, Super Grain should be to maximize sales efforts to the pursuit of profit, but sales and advertising profits is difficult to clarify the relationship between exposure, so in this, Super Grain to seek to maximize advertising exposure.In addition, Super Grain order to simplify the subject, plus a few assumptions:1. The number of ads purchased can be 0 or positive real number.2. Advertising costs and advertising costs to buy are all linear.3. Ad purchase cost, will not interact with each other.

After, Super Grain want to target customers in both, to achieve the least number of viewers, the five million people. So Super Grain to study the various

advertising media to watch the expected number, as follows:

Table 2: Benefit data

Number Reached in Target Category

Target CategoryEach TV

CommercialEach

Magazine AdEach

Sunday Ad

MinimumAcceptable

LevelYoung children 1.2 million 0.1 million 0 5 millionParents of young children 0.5 million 0.2 million 0.2 million 5 million

Again, Claire Syverson brought strongly believe that the promotional coupon interest, so she went to study in the media joined the coupons, the redemption of the coupon the cost, as the table, and their available funds, $ 1,490,000, brought redemption of these coupons.

Table 3: Coupon redemption data

Contribution Toward Required Amount

RequirementEach TV

CommercialEach

Magazine AdEach

Sunday AdRequiredAmount

Coupon Redemption 0 $40,000 $120,000 $1,490,000

In the above limit conditions, Super Grain how to set up a combination of advertising media to achieve maximum advertising exposure is the goal of this problem.This model to:

 

 

 The results obtained are as follows: 

 We can see from the above, the best combination of advertising media:

5 Television commercials, 0.1860465 Advertisements in magazine,12.35465 Advertisements in major newspaper.

The expectations of its biggest exposure: 12788950.

In addition to this, Row 7 of the dual price quite large, we can see if the increase in the number of Television commercials should be able to bring considerable exposure, it is to be analyzed by parametric analysis.

(1) can be seen from above, TV increase in the amount of up to 0.5925926, and the scope of the following, each additional unit of Television commercials, the exposure can increase the amount of 1,163,953.

(2) increasing the TV to 5.5926, and the remaining restrictions are the same, get the optimal solution is:

  This still can be seen in Row 7 of the dual price considerably, so we'll try to increase the TV restrictions.

(3) TV limit is increased to 11.1112 we get:

 

 This discovery, Row 7 is no longer dual price, so we can find, Television commercials, including the scope, expected exposure to 1,163,953, an increase of this slope units; and Television commercials in the range of expected exposure to 175,000, the slope of the unit increased; and Television commercials in the range of expected exposure will not be increased.

After, Super Grain to study very carefully the number of all advertising media, will bring the number of sales, as follows:Table 4: The impact of advertising levels on first-time purchase of Crunchy Start

Numberof TV Spots

Numberof Sales

Number of Magazine Ads

Numberof Sales

Number of Adsin Sunday Supplements

Numberof sales

1 1,000,000 5 700,000 2 1,200,0002 1,750,000 10 1,200,000 4 2,200,0003 2,450,000 15 1,550,000 6 3,000,0004 2,800,000 20 1,800,000 8 3,500,0005 3,000,000 25 2,000,000 10 3,750,000

In this section, in order to simplify the problem, but also added several assumptions:4. Did not see the above table does not include sales of advertising and buy breakfast.5. The table contains only see ads for the first time to buy breakfast, not included purchase of a second after the sales.6. Gross profit for each breakfast, 50 cents.Therefore, this part is to meet the above constraints, the pursuit of maximum profit.

This model to:

 

 The results obtained are as follows: 

We can see from the above, the best combination of advertising media:5 Television commercials, 0.1860465 Advertisements in magazine,12.35465 Advertisements in major newspaper.The maximum margin: 3453343.

Suggestions or other considerations:(1) purchases of advertising should be an integer value. Unless they consider, the ad unit is the 2 minutes or 3 minutes, then there is decimal, such as 0.5, which may represent 60 seconds or 90 seconds range.(2) the purchase of advertising cost function should be concave function, the nonlinear function. Unless this part is to buy advertising time on different channels.(3) different time, different channels of advertising, the cost should be different.(4) advertising design company set the cost of advertising planning, should Gudingchengben, rather than variable costs.(5) expected exposure function, the number of ads to watch function should be concave function, the nonlinear function.(6) single-exposure on the expected point of view, the use of coupons does not increase efficiency; and for the sale of interests, coupons and have their benefits, but this part is not considered to be combined to assess is.(7) is not considered among the three media, the degree of influence each other.

Shenkaoziliao:A theory of marketing principles, Prentice Hall Business Co., Ltd., Taipei, 2004.Chenshang Yong, Xiao Fufeng, Advertising, Prentice Hall Business Co., Ltd., Taipei, 2006.Liu Jianshun, modern advertising, the cause of John Wiley & Sons Ltd., Taipei, 2004.Sun and promising, advertising, network resources, http://www.eshunet.com/.U.S. breakfast cereal market: 2005 Edition, Mintel International Group Ltd,, 2005