You work at an advertising firm and you\'re managing the account of a client. Yo

Question

You work at an advertising firm and you're managing the account of a client. You're helping them plan their advertising for the next month. They have a budget of $35,000 and want you to design an ad campaign that: Includes at least 10 TV commercials Reaches at least 55,000 people Allocates no more than $20,000 to TV ads Maximizes Total Exposure Quality Units The following table shows the number of people reached per ad, the cost per ad. the number of available ads, and Exposure Quality Units (which measures the ad's effectiveness) per ad for the five available types of media: Write out the formulation of a linear optimization model to help you determine the number of each type of ad to purchase in order to maximize the total Exposure Quality Units of the campaign. (You do not need to find the optimal solution to the model you formulate.)

Explanation / Answer

Let the number of ads for each type be, x1, x2, x3, x4, x5

Objective function, To maximize. 60x1 + 85x2 + 50x3 + 40x4 + 20x5

subject to constraint,

1500x1 + 3000x2 + 500x3 + 450x4 + 100x5< 35000

x1 + x2> 10

1000x1 + 2000x2 + 1500x3 + 2500x4 + 300x5> 55000

1500x1 + 3000x2< 20000

x1< 14

x2< 12

x3< 15

x4< 14

x5< 30

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