An Introduction to Management Science 13th Edition by David Anderson,Dennis Sweeney ,Thomas Williams ,Jeffrey Camm, Kipp Martin

Exercise 15

Michigan Motors Corporation (MMC) just introduced a new luxury touring sedan. As part of its promotional campaign, the marketing department decided to send personalized invitations to test-drive the new sedan to two target groups: (1) current owners of an MMC luxury automobile and (2) owners of luxury cars manufactured by one of MMC's competitors. The cost of sending a personalized invitation to each customer is estimated to be $1 per letter. Based on previous experience with this type of advertising, MMC estimates that 25% of the customers contacted from group 1 and 10% of the customers contacted from group 2 will test-drive the new sedan. As part of this campaign, MMC set the following goals:
Goal 1 : Get at least 10,000 customers from group 1 to test-drive the new sedan.
Goal 2 : Get at least 5000 customers from group 2 to test-drive the new sedan.
Goal 3: Limit the expense of sending out the invitations to $70,000.
Assume that goals 1 and 2 are P 1 priority level goals and that goal 3 is a P 2 priority level goal.
a. Suppose that goals 1 and 2 are equally important; formulate a goal programming model of the MMC problem.
b. Use the goal programming computer procedure illustrated in Section 14.2 to solve the model formulated in part (a).
c. If management believes that contacting customers from group 2 is twice as important as contacting customers from group 1, what should MMC do?