I drastically need help with SolvIng this LP model using MS Excel Solver to find the optimal solution, including the optimal number of television, radio, and newspaper advertisements and the budget allocation for each media.

The LP model is already defined alongside Decision Variables and constraints.

Note!!! I think we are supposed to use =SUMPRODUCT() function.

Problem:

The Flamingo Grill is an upscale restaurant located in St. Petersburg, Florida. To help plan an advertising campaign for the coming season, Flamingos management team hired the advertising firm of Haskell & Johnson (HJ). The management team requested HJs recommendation concerning how the advertising budget should be distributed across television, radio, and online advertisements. The budget has been set at $279,000.

In a meeting with Flamingos management team, HJ consultants provided the following information about the industry exposure effectiveness rating per ad, their estimate of the number of potential new customers reached per ad, and the cost for each ad:

Advertising Media	Exposure Rating per Ad	New Customers per Ad		Cost per Ad
Television	90	4,000		$10,000
Radio	25	2,000		$ 3,000
Online	10	1,000		$ 1,000

The exposure rating is viewed as a measure of the value of the ad to both existing customers and potential new customers. It is a function of such things as image, message recall, visual and audio appeal, and so on. As expected, the more expensive television advertisement has the highest exposure effectiveness rating along with the greatest potential for reaching new customers.

At this point, the HJ consultants pointed out that the data concerning exposure and reach were only applicable to the first few ads in each medium. For television, HJ stated that the exposure rating of 90 and the 4000 new customers reached per ad were reliable for the first 10 television ads. After 10 ads, the benefit is expected to decline. For planning purposes, HJ recommended reducing the exposure rating to 55 and the estimate of the potential new customers reached to 1500 for any television ads beyond 10. For radio ads, the preceding data are reliable up to a maximum of 15 ads. Beyond 15 ads, the exposure rating declines to 20 and the number of new customers reached declines to 1200 per ad. Similarly, for online ads, the preceding data are reliable up to a maximum of 20; the exposure rating declines to 5 and the potential number of new customers reached declines to 800 for additional ads.

Flamingos management team accepted maximizing the total exposure rating, across all media, as the objective of the advertising campaign. Because of managements concern with attracting new customers, management stated that the advertising campaign must reach at least 100,000 new customers. To balance the advertising campaign and make use of all advertising media, Flamingos management team also adopted the following guidelines:

• Use at least twice as many radio advertisements as television advertisements.
• Use no more than 20 television advertisements.
• The television budget should be at least $140,000.
• The radio advertising budget is restricted to a maximum of $99,000.
• The online budget is to be at least $30,000.

A B D E F G H J 1 2 3 4 5 6 Prior to exposure Advertizing Media Exposure Rating New Customers per Ar Cost per Ad Television 90 4000 10000 Radio 25 2000 3000 Newspaper 10 1000 1000 After exposure Advertizing Media Exposure Rating New Customers per Ar Cost per Ad Television 55 1500 10000 Radio 20 1200 3000 Newspaper 5 800 1000 7 8 9 Budget: 279000 exposure and new customers decrease after: 10 TV ads 15 radio 20 newspaper 10 >= 11 Let: 12 T1 number of TV adds before 10 ads 13 T2 number of TV adds after 10 ads 14 R1 number of radio adds before 15 ads 15 R2 number of radio adds after 15 ads 16 N1 number of newspaper adds before 20 adds 17 N2 number of newspaper after 20 adds 18 Objective function: 19 Maximize Z = 90T1 + 55T2 + 25R1 + 20R2 + 10N1 + 5N2 20 Subject to: 21 T1 = 100,000 26 R1 + R2 >= 2(T1+T2) 27 T1+ T2 = 140,000 29 3,000R 1 + 3,000R2 = 30,000 31 Non negativity constraint: 32 T1, T2, R1, R2, N1, N2 >= 0 33 Cost Constrains: 0 140000 0 99000 0 30000 Budget Constrain 0 0 = 2(T1+T2) =