Chapter 6.5, Problem 40E

Many of Exercises 29-40 are similar or identical to ones in preceding exercise sets. Use duality to answer them.

Risk Management The Grand Vizier of the Kingdom of Um is being blackmailed by numerous individuals and is having a very difficult time keeping his blackmailers from going public. He has been keeping them at bay with two kinds of payoff: gold from the Royal Treasury and political favors. Through bitter experience, he has learned that each gold payoff gives him peace for an average of about 1 month, and each political favor seems to earn him about a month and a half of reprieve. To maintain his flawless reputation in the court, he feels that he cannot afford any revelations about his tainted past to come to light within the next year. Thus, it is imperative that his blackmailers be kept at bay for at least 12 months. Furthermore, he would like to keep the number of gold payoffs at no more than one quarter of the combined number of payoffs because the outward flow of gold bars might arouse suspicion on the part of the Royal Treasurer. The gold payoffs tend to deplete the Grand Vizier’s travel budget. (The treasury has been subsidizing his numerous trips to the Himalayas.) He estimates that each gold bar removed from the treasury will cost him four trips. On the other hand, because the administering of political favors tends to cost him valuable travel time, he suspects that each political favor will cost him about two trips. Now, he would obviously like to keep his blackmailers silenced and lose as few trips as possible. What is he to do? How many trips will he lose in the next year?