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# Michigan Motors Corporation Goal Programming

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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.

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#### Solution Preview

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+)
Subject ...

#### Solution Summary

This solutioin demonstrates the required programming model with a brief discussion. This solution is completed in plain text.

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