Question:

(Media selection problem) The advertising director for Diversey Paint and Supply, a chain of four retail stores on Chicago's North Side, is considering two media possibilities. One plan is for a series of half- page ads in the Sunday Chicago Tribune newspaper, and the other is for advertising time on Chicago TV. The stores are expanding their lines of do-it-yourself tools, and the advertising director is interested in an exposure level of at least 40% within the city's neighborhoods and 60% in northwest suburban areas.

The TV viewing time under consideration has an exposure rating per spot of 5% in city homes and 3% in the northwest suburbs. The Sunday newspaper has corresponding exposure rates of 4% and 3% per ad. The cost of a half-page Tribune advertisement is $925; a television spot costs $2,000.

Diversey Paint would like to select the least costly advertising strategy that would meet desired exposure levels.

(a) Formulate using LP.

(b) Solve the problem.

Let X1 = the number of newspaper ads placed

X2 = the number of TV spots purchased

Objective function: Minimize, 925X1 + 2,000X2 (minimize cost)

Subject to: .04X1 + .05X2 >= .4 (city exposure)

.03X1 + .03X2 > =.6 (suburb exposure)

X1, X2 < =0 (non-negativity constraints)