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 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 at $1.0 per letter
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.
Let x1 = number of letters mailed to group 1 customers
Let x2 = number of letters mailed to group 2 customers
Minimize P1 (d1-) + P1 (d2-) + P2 (d3+)
This solutioin demonstrates the required programming model with a brief discussion. This solution is completed in plain text.