Question

(20 points total) An ad campaign for a new snack chip will be conducted in a limited geographical area and can use TV time, radio time, and newspaper Information about each medium is shown below. Medium Cost/Ad () # of potential customers reached Exposure Quality TV 500 10000 30 3000 Radio 200 40 400 5000 Newspaper 25 Formulate a linear program that maximizes the number of potential customers reached and satisfies the constraints mentioned in parts (b), (c), (d) and (e). You do not have to solve. a. (4 points) Clearly define your decision variables and then formulate the objective function b. (4 points) The number of TV ads cannot exceed the number of radio ads by more than four. Formulate a constraint in the space below. c. (4 points) The assigned budget for the advertising campaign is $10000. Formulate a budget constraint in the space below. d. (4 points) The snack chip manufacturer wants to achieve an exposure quality of at least 1000. Formulate a constraint. e. (4 points)Finally formulate a constraint for the condition that the number of radio advertisements cannot exceed 40% of the total number of advertisements.

Answer 1

a) Let the number of TV ad campaign be x

Let the number of Radio ad campaign be y

Let the number of Newspaper ad campaign be z

Objective Function, Maximize Z = 10000*x + 3000*y + 5000*z

b) The difference between the number of TV ads and Radio ads by more than 4

x - y <= 4

c) The budget constraint for the problem

500*x + 200*y + 400*z <= 10000 (Total budget is less than $10000)

d) The minimum exposure quality must be 1000

30*x + 40*y + 25*z >= 1000

e) The number of radio advertisements cannot exceed the total number of advertisements

y <= 0.4(x+y+z)

y <= 0.4x + 0.4y + 0.4z

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