A major auto manufacturer is planning the marketing campaign to introduce its new Bambi model of hybrid sport utility vehicle. Bambis will be introduced with a television advertising campaign totaling $200 million. The table below shows the 3 kinds of programs being considered for placement of the ads, including the cost per 30-second (unit)

commercial and the number of viewers exposed in each of the market segments. No more than 50%

of the budget should be spent on any one type of program. Within these limits the company has set goals of 3,000 million under-30 exposures from the campaign, 5,000 million age 30–55 male exposures, and 3,400 million age 30–55 female exposures.

Program Type Unit Cost

($ million)

Exposures per Unit

(millions)

Under 30 30–55 Male 30–55 Female Desperate Housewives 2.2 24 12 37 Law and Order 2.5 27 42 11 Comedy Central 0.5 19 16 6

(a) Formulate a Linear Goal Program to help the manufacturer decide how to optimally place their ads. Weight all goals equally.

Be sure to define all decision variables, and annotate objectives and constraints to indicate their meaning.

(b) Obviously numbers of commercial showings in

(a) must be integer, but it is good OR modeling to treat them as continuous.

Briefly explain why.

(c) Enter and solve the your goal of

(a) with class optimization software.