1 September 1999
Technical Mathematics, Inc.
Suite 4, Strawmarket Business Plaza
Lonlinc, SK 04685
As part of our continuing efforts to address the water needs of the state, we are here at the Locodora State Water Agency trying to get a handle on the annual rainfall in our state. This is, of course, complicated by the fact that the state is fairly large---approximately a 375 mile by 275 mile rectangle. We need therefore to use some sort of representative sample, and are measuring the rainfall at a number of recording stations scattered appropriately about the state. While it would be desirable to have a huge number of these, recent cuts in the state budget to subsidize tax breaks for such underpriviledged groups as those making between $149,997 and $150,000 makes the cost of their construction and staffing prohibitive. We have therefore a much smaller number of stations (currently, eight), to which we hope to add in the future. From the data from these stations, we need to obtain accurate, scientific estimates for both the total rainfall in the state and the rainfall at arbitrary locations in the state. It is to obtain such estimates that we are contacting you.
The locations of the eight stations that we have currently established are shown in table 1 below, in which coordinates are measured relative to an origin located at the southwest corner of the state. The recorded annual rainfall at each station is also shown in this table.
|Location||(77.5, 212.5)||(145, 227.5)||(247.5, 215)||(92.5, 100)|
|Location||(137.5, 145)||(185, 157.5)||(262.5,157.5)||(150, 32.5)|
We look forward to receiving your solution to this problem, which should be sufficiently general as to be applicable to the case presented here, which has few recording stations, and to the possibility of more stations (e.g., on the order of 200--300). It should also include some estimate for the possible error in your calculations. That said, it is with indescribable anticipation that we wait for your presentation of your solution, which will be on the 15th or 17th of September, and final papers, which are due on the 20th of the month.
Yours most sincerely,
Director, Locodora SWA