These payments are designed to increase the probability that Salt Lake City will be awarded the 2002 Olympic Games. Let X1, X2, X3, and X4 represent the dollar amount to each of the four categories and assume the link between the payments and the chance of a successful bid is given by the equation:

In this problem, we see that payments to the NOC Assistance Program will increase the probability of a successful bid the most. But there are constraints that have to be met. They are:

1. At least 30% of the budget will be payments to specific IOC members (Type 1).
2. No more than $2.5 million can be in the form of "other" payments (Type 2).
3. All money should be spent.
4. All records must be destroyed after the payments have been made.

Solve this problem using linear programming.

*The investigation by SLOC revealed that the bid committee had established a financial assistance programme, described as an "NOC Support Program," purportedly aimed at developing countries. This programme was apparently established in late 1991 or early 1992, after the close loss which Salt Lake City experienced with respect to the 1998 Olympic Winter Games, which were awarded to Nagano. It is not clear exactly to what degree the existence of the programme was known by the bid committee as a whole, although we are advised by SLOC that it appears as a line item in the audited financial statements of the bid committee. It seems clear from the evidence given, to date, by SLOC that the programme was administered principally by Thomas Welch ("Welch"), the president of the bid committee and later president of SLOC until his resignation in 1997. David Johnson ("Johnson"), then Executive Vice-President of SLOC and one of the few members of the bid committee who had survived the transition from bid committee to Organizing Committee of the Olympic Games (OCOG), was aware of the existence of the programme and active in its implementation.