Michigan Motors Corporation $($MMC$)$ just introduced a new luxury touring sedan. As part

of its promotional campaign, the marketing department decided to send personalized invita$-$

tions 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$\text{'}$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 $14\mathrm{.}2$ 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$?$