Problem 9 ABC company is launching a new luxury car and the marketing department decided to send personalized invitations to test drive the new car to 2 target groups: (1) current owners of an ABC car and (2) owners of luxury cars of a ABC competitor. The cost of sending out letters is $1/letter. Based on previous experience, ABC estimates that 25% of the customers contacted from group 1 and 10% of customers from group 2 will actually do the test drive. ABC has the following goals: Goal 1: Get at least 10, 000 customers from group 1 to test drive the new car Goal 2: Get at least 5000 customers from group 2 to test drive the new car. Goal 3: Limit the expense of sending out invitations to $70,000 Goals 1 and 2 are the most important but ABC feels that contacting group 2 is twice as important as group 1. Goal 3 is the least important. Formulate a pre-emptive goal programming model for the problem. Solve the model using LINGO. What is the number of invitations to send out to each group? Which goals are violated and by how much? Attach your LINGO code and output. (15 marks) Problem 9 ABC company is launching a new luxury car and the marketing department decided to send personalized invitations to test drive the new car to 2 target groups: (1) current owners of an ABC car and (2) owners of luxury cars of a ABC competitor. The cost of sending out letters is $1/letter. Based on previous experience, ABC estimates that 25% of the customers contacted from group 1 and 10% of customers from group 2 will actually do the test drive. ABC has the following goals: Goal 1: Get at least 10, 000 customers from group 1 to test drive the new car Goal 2: Get at least 5000 customers from group 2 to test drive the new car. Goal 3: Limit the expense of sending out invitations to $70,000 Goals 1 and 2 are the most important but ABC feels that contacting group 2 is twice as important as group 1. Goal 3 is the least important. Formulate a pre-emptive goal programming model for the problem. Solve the model using LINGO. What is the number of invitations to send out to each group? Which goals are violated and by how much? Attach your LINGO code and output. (15 marks)