Goal programming model

Michigan Motors Corporation (MMC) has just introduced a new luxury touring sedan. As part of its promotional campaign, the marketing department has decided to send personalized invitations to test drive the new sedan to two target groups: 1) Current owners of an MMC Luxury car and 2) owners of luxury cars manufactured by one of MMC competitors. The cost of sending a personalized invitation to each customer is estimated to be $1 per letter. Based on previous experience fro this type of advertising. MMC estimate that 25% of the customers contacted from group 1 and 10% of the customers contracted from group 2 will test drive the new sedan. As part of this campaign, MMC has 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 5,000 customers from group 2 to test drive the new sedan.
Goal 3: Limit the expense of sending out the initiations to $70,000.

Assume that goals 1 and 2 are P1 priority level goals and that goal 3 is a P2 priority level goal.

a) Suppose that goals 1 and 2 are equally important; formulate a goal programming model of the MMC problem.

c) If management believes that contacting customers from group 2 is twice as important as contacting customers from group 1, what should MMC do?