Linear Programmin: Formulation Media Selection A firm is working on developing i

ID: 360931 • Letter: L

Question

Linear Programmin: Formulation

Media Selection A firm is working on developing its marketing strategy for a product and accordingly, wishes to determine the number of ads to be placed in each advertising medium per month. The total monthly advertising budget is $1,000,000. The following choices are available: Advertising Medium Cost/Ad Expected Exposure/Ad Television $50,000 1,000 Radio $5,000 300 Newsweek $300 20 SF Chronicle $200 15 The firm decides that television advertising should be limited to $500,000 per month. Its objective is to maximize the total expected exposure per month.

Just set up the variables and constraints etc.

Explanation / Answer

Variables

We need to decide the number of ads to be placed in each advertising medium per month. Hence let:

xi be the number of ads to be placed in each advertising medium i (i=1,2,3,4 for Television, Radio, Newsweek and SF Chronicle respectively) per month where xi >=0 i=1,2,3,4

Advertising Medium

Cost/Ad ($)

Expected Exposure/Ad

Number of Ads

Television

50,000

1,000

Radio

5,000

300

Newsweek

300

SF Chronicle

200

Constraints

50,000 x1 + 5,000 x2 + 300 x3 + 200 x4 <= 1,000,000

50,000 x1 <= 500,000

Objective

The objective is to maximise the total expected exposure per month, i.e.

maximise 1000 x1 + 300 x2 + 20 x3 + 15 x4

The basic assumption is that at least 1 ad needs to be placed in each medium.