M230 Test III Fall 1997 Solutions

1. (a)
x = 27; y = 21

(b) x=26; y=26

(c) Thus, x is larger in the solution to the system a) than in b).

2. R3-R1 R1-2R3
R2+R3 -R3

Thus

3. The Feasible set is shaded:

The maximum x-value is 24 at the corner (24, 8). The maximum y value is 16 at the corner (8,16). The maximum x+y value is 32, at the corner (24,8). Thus x and x+y assume their maximum at the same corner point; y at a different corner point.

4. (a) possible # of red balls: 0, 1, 2, 3.
Transition diagram: (Four states)
(b) Transition matrix: (States in order 0-1-2-3 for rows and columns.)
(c) Probability in state 1 after one draw is 0, the underlined entry in P.
(d)

So the probability of state # 1 after 2 draws is . (underlined in ).

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