Math 230 Final examFall 1997 Solutions

1. (a)

(b)

(c) impossible. a and a matrix cannont be added.

(d)

(e) impossible. a matrix cannot be multipled by a matrix in that order.

(f)

2.
x +2y = 20 x + 2y + a = 20
x + y + z + u = 18
maximize z

maximize z -Ma f-z +Ma = 0

y=10, z=8, x=0, f=8 The maximum z value is 8.

3. The number of ways to assign pilots to twins
The number of ways to assign pilots to singles

Pr(none of the twin-engine rated pilots ends up flying a single) =

4.(a) x + y = 8
x - y = 2

(b)

so

(c)
x + y = 8
x - y = 2 (add) 2x = 10 x = 5

Plugging x = 5 into one of the original equations we get 5 + y = 8 so y = 3.

5. X = 1, 2, 3. Note that X cannot be 0 or 4 since there are only red balls in the red urn and no red balls in the green urn.

6. (a) Transition diagram: (Four states)

(b) Transition matrix: (States in order R-G-B-Y for rows and columns.)
(c) = =

7.
G = the event of picking out of the green urn
R = the event of picking out of the red urn
B = the event of picking out of the blue urn
Y = the event of picking out of the yellow urn
g = picking a green ball
r = picking a red ball
b = picking a blue ball
y = picking a yellow ball

Replace each with . ex.

8. B Y

and and .

So,