AMS 210.03
Final Exam
1.
Two factories, with production levels x
1
andx
2
, produce cars, trucks, and vans according to the
following formulae:
Cars = 2x
1
+ x
2
Trucks=x
1
+ x
2
Vans =
x
2
If the demand is 200 cars, 100 trucks, and 100 vans, find the values for x
1
and x
2
and
resulting supplies
of cars, trucks, and vans that comes as close as possible to the demand (minimizing the distance
between the demand vector and the supply vector).
2.
A statistical experiment is run on a machine that makes paper bags.
The settings of two control
dials, dial A and dial B, affect the quality rating of the bags.
We use the regression model z=qx+ry+s,
where z is the quality rating, x is the dial A setting, and y is the dial B setting.
The results of the
experiment are:
z
x
y
Quality
Dial A
Dial B
4
1
1
6
2
1
5
1
3
3
0
3
Find the values of the regression coefficients q, r, s.
(Hint: columns are orthogonal).
3.
Let A=
2
0
1
6
2
4
3
2
1
3
2
0
a)
Find a basis for the range of A.
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 Spring '08
 FRIED
 Linear Algebra, Markov chain, Quality Rating, regression model z=qx+ry+s

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