Hello, I have seen many posts about this question but I would like to have a det

Question

Hello, I have seen many posts about this question but I would like to have a detailed explanation of how to use these numbers and how to use excel to figure out this question. Thank you!

The Westchester Chamber of Commerce periodically sponsors public service seminars and programs. Currently, promotional plans are under way for this year's program. Advertising alternatives include television, radio, and newspaper. Audience estimates, costs, and maximum media usage limitations are as shown: Television Radio Constraint Audience per advertisement Cost per advertisement Maximum media usage Newspaper 100000 $1400 10 18000 $190 10 40000 $600 20 To ensure a balanced use of advertising media, radio advertisements must not exceed 50% of the total number of advertisements authorized. In addition, television should account for at least 10% of the total number of advertisements authorized a. If the promotional budget is limited to $26,100, how many commercial messages should be run on each medium to maximize total audience contact? What is the allocation of the budget among the three media? If required, round your answers to the nearest dollar Let T = number of television spot advertisements number of radio advertisements N number of newspaper advertisements Budget ($) Total Budget$ What is the total audience reached? Round your answer to the nearest whole number b. By how much would audience contact increase if an extra $100 were allocated to the promotional budget? Round your answer to the nearest whole number

Explanation / Answer

Let assume that if advertisement is done to maximum posible limit.

As per the given data , 10 times usage of television can be done , 10 times usage of radio can be done , and 20 times usage of newspaper can be done .

So the cost of television = $ 1400 ( cost per advertisement) * 10 = $ 14000 and number of customers for ten times prmotion through television = 100000 ( customers per advt ) * 10 = 1000000

Similarly we calculate for radio and newspaper

Below is the table given

As per the table the maximum usage requires budget of $ 27900 . But the budget available is $26100.

Now as per the conditions given , we can use the radio advertisements to maximum 50% of total.

So lets assume that radio is used to maximum limit ( 10 ) . So the cost is $190 * 10 = $ 1900 .

So the balance budget remaining is $ 26100- $ 1900 = $24200.

Now The balance budget should be used in such a way that it should be completely utilised and there is maximum output.

As per given condition ,we should use television at least 10% of total advertisements and maximum limit is 10 .

So the cost of telivision is $1400 * 10 = $ 14000

So balance bduget is $ 26100 - $ 1900 - $ 14000 = $ 10200.

So the total number of times the newspaper is used = $10200 ( balance budget ) / $ 600 ( cost per advt. ) = 17 .

So the total number of advertisements = 10 ( Television ) + 10 ( Radio ) + 17 ( Newspaper ) = 29

If $ 100 is allocated to promotional budget, then it does not make much different because, if changes are made in the advertisement usage of any of these medium to balance the budget , the number of customers will be reduced.

maximum Media usage Cost per advt. Total Cost Num. of customers per advt Maximum customers Television 10 1400 14000 100000 1000000 Radio 10 190 1900 18000 180000 Newspaper 20 600 12000 40000 800000 Total 40 27900 1980000

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