Mr. Baker wants to send numerous aid packages to Cuban citizens. Three different types of packages are available. The basic package costs $300, weighs 120 pounds, and aids 30 people. The advanced package costs $350, weighs 180 pounds, and aids 35 people. The supreme package costs $720, weighs 220 pounds, and aids 54 people. Mr. Baker has several goals. First, he wants to aid at least 2,2 million citizens. Second, he wants at least 3,000 of the aid packages sent to Cuba to be the supreme packages. Third, he wants to keep the cost of aiding Cuba below $20 million. Mr. Baker places different levels of importance on his three goals. The most important goal is keeping costs down, he decides to penalize his plan by 1 point for every $1 million above his $20 million goal. The second most important goal is ensuring that at least 3,000 of the aid packages sent to Cuba are supreme packages, he decides to penalize his plan by 1 point for every 1,000 packages below his goal of 3,000 packages. Finally, the least important goal is reaching at least 2,2million people. He therefore decides to penalize his plan by 7 points for every 100,000 people below his 20 percent goal.

He is only able to send a maximum of 40,000 packages. He cannot ship more that 6 million pounds of cargo. Finally, when sending medicine, for every 100 supreme packages, he must send one doctor to Cuba at a cost of $33,000 per doctor.

a) Formulate the problem as a preemptive goal programming. b) Mr. Baker reevaluates the levels of importance he places on each of the three goals. To sell his efforts to potential donors, he must show that his program is effective. Donors generally judge the effectiveness of a program on the number of people reached by aid packages. Mr. Baker therefore decides that he must put more importance on the goal of reaching at least 20 percent of the population. He decides to penalize his plan by 10 points for every half a percentage point below his 20 per- cent goal. The penalties for his other two goals remain the same. Formulate the problem under this scenario. c) Mr. Baker realizes that sending more doctors along with the supreme packages will improve the proper use and distribution of the packages contents, which in turn will increase the effectiveness of the program. He therefore decides to send one doctor with every 75 supreme packages. The penalties for the goals remain the same as in part (b). Write down the changes in the mathematical formulation of (b)?