ADVERTISING
Response to the following problem:
Print Media Advertising (PMA) has been given a contract to market Buzz Cola via newspaper ads in a major Southern newspaper. Full-page ads in the weekday editions (Monday through Saturday) cost $2000, whereas on Sunday a full-page ad costs $8000. Daily circulation of the newspaper is 30,000 on weekdays and 80,000 on Sunday. PMA has been given a $40,000 advertising budget for the month of August. The experienced advertising executives at PMA feel that both weekday and Sunday newspaper ads are important; hence, they wish to run the equivalent of at least eight weekday and at least two Sunday ads during August. (Assume that a fractional ad would simply mean that a smaller ad is placed on one of the days; that is, 3.5 ads would mean three full-page ads and one one-half page ad. Also assume that smaller ads reduce exposure and costs proportionately.) This August has 26 weekdays and 5 Sundays.
a. If the objective is to maximize cumulative total exposure (as measured by circulation) for the month of August, formulate and solve a linear program to determine the optimal placement of ads by PMA in the newspaper during August. Comment on the validity of the "no interaction" assumption of linear programming for this model.
b. Explain why the constraints on the maximum number of weekday ads and the maximum number of Sunday ads are both redundant.
c. Suppose the minimum restriction for Sunday ads were eliminated. What would be the new optimal solution? What would be the reduced cost for Sunday ads?