The advertising alternatives for a company include televisio

The advertising alternatives for a company include television, radio and newspaper advertisements. The costs and estimates for audience are given in Table 9.2 The local newspaper limits the number of weekly advertisements from a single company to ten. Moreover, in order to balance the advertising among the three types of media, no more than, half of the total number of advertisements should occur on the radio, and at least 10% should occur on television. The weekly advertising budget is $18,200. How many advertisements should be run in each of the three types of media to maximize the total audience?

Solution

Audience 100000 40000 18000 1000000X+40000y+18000z cost per audience 0.02 0.015 0.016666667 Objective is to maximise z 1000000X+40000y+18000z 200x+600y+300z<=18200 2x+6y+3z<=182 Constraints: y<=10 z<=(x+y+z)/2 x>=(x+y+z)/10 Cost per audience is the least for newspaper Hence maximum 10 should be allotted to newspaper y =10 z<= (x+10+z)/2 z<=x+10 x>=(x+y+z)/10 10x>=x+y+z z<=9x+10 Together z <=x+10 2x+6y+3z<=182 becomes 2x+3z<=122 Next to y for Z cost is minimum 2x+27x+30<=122 29x<=92 Hence x =3, y = 10 z =13 is the optimum mix x<=3 z<=13 Maximum audience 100000(3)+600(10)+18000(13) 540000