Formulation of LPP - 12 Marketing Management - Advertising Mix
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An advertising company, on behalf of one of its client, wants to plan an advertising campaign for three different medias: TV (Day Time and Prime Time separately), Radio and Print Media. The purpose of the advertising is to reach as many potential customers as possible. The following are the results of a market study:
1) Cost of one advertising unit
TV-Day Time: Rs. 1,00,000
TV-Prime Time: Rs. 1,87,500
Radio: Rs. 75,000
Print Media: Rs. 37,500
2) Number of potential customers reached per advertising unit:
TV-Day Time: 4,00,000
TV-Prime Time: 9,00,000
Radio: 5,00,000
Print Media: 2,00,000
3) Number of women customers reached per advertising unit
TV-Day Time: 3,00,000
TV-Prime Time: 4,00,000
Radio: 2,00,000
Print Media: 1,00,000
The company does not want to spend more than Rs. 20,00,000 on advertising. It is further required that -
(i) At lest two million exposures take place among women.
(ii) The cost of advertising on TV be limited to Rs. 12,50,000.
(iii) On TV, at least three advertising units be bought on Day Time and two units on Prime Time.
(iv) The number of advertising units on Radio and Print Media should each be between 5 and 10.
Formulate this problem as an LPP to maximize the potential customer reach.
General Mathematical Model of LPP:
The number of problems, showing how to model them by the appropriate choice of decision variables, objective, and constraints. Any linear programming problem involving more than two variables may be expressed as follows:
Find the values of the variable x1, x2,............, xn which maximize (or minimize) the objective function
Z = c1x1 + c2x2 + .............. + cnxn
subject to the constraints
a11x1 + a12x2 + ............. + a1nxn ≤ b1
a21x1 + a22x2 + ............. + a2nxn ≤ b2
........................
am1x1 + am2x2 + .............. + amnxn ≤ bm
and meet the non negative restrictions
x1, x2, ..., xn ≥ 0
a) A set of values x1, x2,.. xn which satisfies the constraints of linear programming problem is called its solution.
b) Any solution to a linear programming problem which satisfies the non negativity restrictions of the problem is called its feasible solution.
c) Any feasible solution which maximizes(or minimizes) the objective function of the linear programming problem is called its optimal solution
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