Answer to Question #106115 in Operations Research for Riya

Question

An advertising agency whishes to reach two types of audiences: customers with
annual income greater than one lakh rupees (target audience A) and customers
with annual income of less than one lakh rupees (target audience B). The total
advertising budget is ` 2,00,000. One programme of TV advertising costs ` 50,000;
one programme of radio advertising costs ` 20,000. For contract reasons, at least
three programmes should to be on TV and the number of radio programmes must be
limited to 5. Surveys indicate that a single TV programme reaches 4,50,000
propective customers in target audience A and 50,000 in target audience B. One
radio programme reaches 20,000 prospective customers in target audience A and
80,000 in target audience B. Formulate it as a LPP and solve it graphically to
maximize the total reach for the programmes.

Answer 1

Solution.

A single TV program reaches out to 4,50,000 + 50,000 = 5,00,000 customers.

A single radio program reaches out to 20,000 + 80,000 = 1,00,000 customers.

Suppose X number of TV programs were made, and Y number of TV programs.

The total number of customers these programs can reach out to is:

5,00,000 X + 1,00,000 Y

Maximize Z = 5,00,000 X + 1,00,000 Y

Total advertising budget available is Rs. 2,00,000

One TV program costs Rs. 50,000; so X TV programs will cost 50,000 X

One radio program costs Rs. 20,000; so Y radio programs will cost 20,000 Y

So the total cost should be limited as follows:

50,000 X + 20,000 Y ≤ 2,00,000

X ≥ 3 and Y ≤ 5

Maximize Z = 5,00,000 X + 1,00,000 Y

So the LPP formed is as follows:

Maximize Z = 5,00,000 X + 1,00,000 Y

Subject to 50,000X+20,000Y≤2,00,000

X≥3

Y≤5

X,Y≥0

Answer:Maximize Z = 2,000,000; X=4;Y=0.