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.