Question

Two advertising media are being considered for promotion of a product. Radio ads cost $400 each, while Newspaper ads cost $600 each. The total budget is $7,200 per week. The total number of ads should be at least 15, with at least 2 of each type. Each newspaper ad reaches 6,000 people, while each radio ad reaches 2,000 people. The company wishes to maximize the number of people that are reached while meeting all the constraints stated. Write the LP formulation to determine the optimal number of ads of each type to be used.

Answer 1

Since only formulation is asked, we will not solve the LPP after formulation.

Let the number of Radio ads be r and no. of newspaper ads be n

Total reach to people = 2000 * r + 6000 * n

We have to maximize this reach. Hence, we get the objective function as:

Maximize Total Reach = 2000r + 6000n

Total cost = 400 * r + 600 * n

Total Budget = $7,200

Hence, we get constraint as:

400r + 600n <= 7200..........Constraint for total budget available

r + n >= 15..........................Minimum number of total ads required.

r >= 2..................................Minimium number of radio ads required

n >= 2..................................Minimium number of newspaper ads required

r, n >= 0...............................Non-negativity constraints since no. of radio ads and newspaper ads cannot be negative

Hence, we get the formulation as:

Maximize Total Reach = 2000r + 6000n

400r + 600n <= 7200

r + n >= 15

r >= 2

n >= 2

r, n >= 0

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