Problem 25			Due April 10, 2000

In many industrial plants there are releases of controlled 
material into waste streams, which then must be 
processed at municipal treatment plants.  In order to 
determine the compliance and/or cost of such releases 
(the city typically bills the plant for cleaning up the waste), 
it is important to determine the amount released, and to 
this end there are municipal monitoring facilities.  At a 
particular plant, the monitoring station is supposed to 
measure the flow rate and concentration every hour (the 
plant has 24 hour continuous operations), which can be 
integrated to obtain the total release for each day.  
Unfortunately, the flow rate monitor jammed, and 
missed two consecutive readings in the morning, and one 
reading in the afternoon.  The concentration detector 
continued to function, however, so there was no missing 
data on concentration.

In this problem, suppose you work for the city and are 
deciding how much to bill the plant.  To determine this, 
you need to have an accurate estimate of how much waste 
was released.  I want you to develop an algorithm which 
accurately estimates the release for that day, and also 
provides estimates for the uncertainty (both algorithm and 
random error) in this value.  Remember that you might 
have to defend your bill to the company!  State all the 
approximations and assumptions that you are using, and 
also offer suggestions about what additional 
measurements you might want to make to further reduce 
your uncertainty.  Note that there is no one right answer to 
this problem - but some answers are better than others!  
Techniques you might want to use include regression, to 
get a feel for the randomness of the data, and interpolation.

The flow rate and concentration data for the day in question 
is given below:

	Hour	Conc.		Flow Rate
	1	6.0674		4.2844
	2	5.9325		6.4692
	3	8.1253		8.0648
	4	7.8858		10.4524
	5	5.3535		*****
	6	6.1909		*****
	7	4.6892		8.5155
	8	2.3643		6.3340
	9	2.3273		4.4329
	10	2.5766		2.7618
	11	3.3133		2.5798
	12	5.7258		3.2963
	13	5.9117		4.5298
	14	9.7813		6.6405
	15	7.8636		8.2091
	16	7.7120		*****
	17	7.5668		10.7833
	18	5.0593		10.1449
	19	3.4044		8.4611
	20	1.5696		6.5678
	21	2.2944		4.7942
	22	1.0657		2.5951
	23	4.2143		2.6029
	24	6.6236		2.5862