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Question
An advertising company wishes to plan its advertising strategy in three different media-television,radio and magazines.The purpose of advertising is to reach as large a number of potential customers as possible.Following data have been obtained from market survey:
Strategies Television Radio Magazine-I Magazine-II Cost of an advertising company Rs.30,000 Rs.20,000 Rs.15,000 Rs.10,000 No.of potential customers reached per unit 2,00,000 6,00,000 1,50,000 1,00,000 No.of female customers reached per unit 1,50,000 4,00,000 70,000 50,000
The company wants to spend not more than Rs.4,50,000 on advertising.Following are the further requirements that must be met:
(i)at least 1 million exposures take place among female customers.
(ii)advertising on magazines be limited to Rs.1,50,000
(iii)at least 3 advertising units be bought on magazine I and 2 units on magazine II
(iv)the number of advertising units on television and radio should each be between 5 and 10.
Formulate an L.P model for the problem.
| Strategies | Television | Radio | Magazine-I | Magazine-II |
| Cost of an advertising company | Rs.30,000 | Rs.20,000 | Rs.15,000 | Rs.10,000 |
| No.of potential customers reached per unit | 2,00,000 | 6,00,000 | 1,50,000 | 1,00,000 |
| No.of female customers reached per unit | 1,50,000 | 4,00,000 | 70,000 | 50,000 |
(i)at least 1 million exposures take place among female customers.
(ii)advertising on magazines be limited to Rs.1,50,000
(iii)at least 3 advertising units be bought on magazine I and 2 units on magazine II
(iv)the number of advertising units on television and radio should each be between 5 and 10.
Formulate an L.P model for the problem.
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Solution
Formulation of Linear programming problem:
Let x1,x2,x3 and x4 denote the number of advertising units to be bought on television,radio,magazineI and magazineII respectively.
The objective is to maximize the total number of potential customers reached.
i.e., Maximize Z=105(2x1+6x2+1.5x3+x4)
Constraints are
on the advertising budget: 30,000x1+20,000x2+15,000x3+10,000x4≤4,50,000
or 30x1+20x2+15x3+10x4≤450
on the number of female customers reached by the advertising campaign:
1,50,000x1+4,00,000x2+70,000x3+50,000x4≥10,00,000
or 15x1+40x2+7x3+5x4≥100.
on expenses on magazine advertising:15,000x3+10,000x4≤1,50,000
or 15x3+10x4≤150
on no. of units on magazines:x3≥3,x4≥2
on no. of units on television:5≤x1≤10 or x1≥5,x1≤10,
on no. of units on radio:5≤x2≤10 or x2≥5,x2≤10,
where x1,x2,x3,x4,each ≥0.
Let x1,x2,x3 and x4 denote the number of advertising units to be bought on television,radio,magazineI and magazineII respectively.
The objective is to maximize the total number of potential customers reached.
i.e., Maximize Z=105(2x1+6x2+1.5x3+x4)
Constraints are
on the advertising budget: 30,000x1+20,000x2+15,000x3+10,000x4≤4,50,000
or 30x1+20x2+15x3+10x4≤450
on the number of female customers reached by the advertising campaign:
1,50,000x1+4,00,000x2+70,000x3+50,000x4≥10,00,000
or 15x1+40x2+7x3+5x4≥100.
on expenses on magazine advertising:15,000x3+10,000x4≤1,50,000
or 15x3+10x4≤150
on no. of units on magazines:x3≥3,x4≥2
on no. of units on television:5≤x1≤10 or x1≥5,x1≤10,
on no. of units on radio:5≤x2≤10 or x2≥5,x2≤10,
where x1,x2,x3,x4,each ≥0.
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