# PreCalculus

Joe Smith is the current governor of New Jersey and 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: money from the State Treasury and political favors. Through bitter experience, he has learned that each payoff in cash gives him peace for an average of about 1 month, while each political favor seems to earn him about a month and a half of reprieve. To maintain his flawless reputation in the State, he feels he cannot afford any revelations about his tainted past to come to light within the next year, when he will announce his bid for Senate. Thus it is imperative that his blackmailers be kept at bay for 12 months. Furthermore, he would like to keep the number of cash payoffs at no more than one-quarter of the combined number of payoffs because the outward flow of cash might arouse suspicion on the part of the State Treasurer. The Governor feels that he can do no more than seven political favors per year without arousing undue suspicion in the State. The cash payoffs tend to deplete his travel budget. (The treasury has been subsidizing his numerous trips to D.C.) He estimates that each time he removed money from the treasury it 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 three 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? Solve both graphically and by using the simplex solver. See rubric for all required elements.

Written in correct report form, neat, intro &  conclusion

Variables clearly defined

Objective & objective function clearly stated

All constraints stated and explained

LP is solved graphically with feasible region  shaded and corner points clearly stated.  Objective function is evaluated at each corner  point.

LP is solved using the Simplex Solver website  with optimal solution stated and explained.

*******************************************************************

GUIDELINES:

(1) You may work with a partner.

(2) This is a report so please write everything in paragraph form with an introduction and conclusion.

(3) Projects should be typed with a cover page. (MathType can be downloaded to write equations)