The advertising company is considering placing advertising on 3 websites of local newspapers promoting their product to people in their twenties, thirties and forties. The number of people exposed to the ads on these websites and the costs of posting the ads are presented in the table below:

New York Times The Age Herald Sun 20-29 6 3 3 30-39 3 4 4 40-49 4 7 3 Costs 1.2 0.8 1

The advertising company wants to achieve the following goals: 1. Generate approximately 40000 exposures among 20 to 29-year-olds 2. Generate approximately 60000 exposures among 30 to 39-year-olds 3. Generate approximately 50000 exposures among 40 to 49-year-olds 4. Spend approximately $12000 on advertising

The company considers Goals 1, 2 and 3 to be twice as important as Goal 4.

d1+, d1- deviation variables for exposures among 20 to 29-year-olds d2+, d2- deviation variables for exposures among 30 to 39-year-olds d3+, d3- deviation variables for exposures among 40 to 49-year-olds d4+, d4- deviation variables for spendings on advertising

x1 - Number of ads in New York Times x2 - Number of ads in The Age x3 - Number of ads in Herald Sun

MIN: 2(d1+ + d1-)/40000 + 2(d2+ + d2-)/60000 + 2(d3+ + d3-)/50000 +(d4+ + d4-)/12000

S.T: 6x1 + 3x2 + 3x3 - d1+ + d1- = 40000 3x1 + 4x2 + 4x3 - d2+ + d2- = 60000 4x1 + 7x2 + 3x3 - d3+ + d3- = 50000 1.2x1 + 0.8x2 + 1x3 - d4+ + d4- = 12000

xi, dj+, dj- >=0 [12:08 PM, 8/23/2022] Iraj Azam RMIT: What is the optimal value of the objective function? Hint: The answer to this question is between 0.28 and 0.31.