McL 151 Assign 5 KEY

# McL 151 Assign 5 KEY - [I ME(fr NAME_1 W Math 151 A03&...

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Unformatted text preview: ._ // [I ME: (fr NAME: \. '\_1 W: Math 151 A03 & A04 Assignment #5 DUE: WEDNESDAY, MARCH 24”“, 2010 At the START 0t CLASS — NO EXCEPTIONS! UNSTAPLED ASSIGNMENTS WILL NOT BE ACCEPTED*** ANSWERS ALONE WILL EARN YOU NO CREDIT. ALL RELEVANT WORKINGS MUST BE SHOWN IN FULL. COMPLETE EACH UESTION AS IF YOU WERE PRESENTING YOUR SOLUTION IN THE CONTEXT of an EXAM. 1. Which of the following matrices are stochastic? [2 Marks] 1 0 0 0 0 1 0 0 .1 1/3 1/3 1/6 a) [0 5 5] b) »—5 0 1.5 c) .5 0 1.5 d) 0 1 0 ' ' .2 .2 .6 .2 .2 .6 1/4 1/2 1/4 Write the CAPITAL LETTER to indicate your answer choice in the Space provided at the bottom of the page. A) None B) Only (a) C) Only (b) D) Only (c) E) Only (d) F) a & b G) a & c H) a & d I) b & c J) b & d K) c & d U mb&c M) a, c & d N) b, c & d 0) All 2. Consider the objective function A = 10y — x subject to: y—xal 431+?3‘3220 x_s3 x31 6% a2:- a,» a) Provide a clearly and fully labelled graph indicating the axes, the equations of all lines drawn, the feasible region, as well as the co—ordinates of all corner points of the feasible region. [\$Marks] b) Determine Whether or not the objective function has a maximum or a minimum value (you should make it very clear whether it is a maximum or minimum), give the value and indicate where it occurs. ['3 Marks] [ I, 1+: - 3 l' -3 _ I ,r , n "L l __ ,C —.- » l tr ,7“ :1— 1 _ _ ya u i? :} ff! ’ a, :7) ( n5, ’1: ."\. 1‘24; ‘:«"§liv\rl.r'( *5 3 7 71 ~l"l '5 "i‘ .f a '1 -= '2 ‘ S ‘f‘ ,- Ytﬁur € «x “ , :2 6% 0’ [4 i l J »r ’ Hi 25 367(2 if /7, / I) ~\ a r” L: C L‘ It fl 0 /‘ ‘ ‘ .- f 5-5:, ‘2 Ni \ L'\.. \ M‘s—wry”. Ni/A'i L’— C' a" ilk IF]: ’4}- k 'r‘\_ ‘. Wm tan-4.. \q/ou- ll “- r- i- ‘2: 3 0'. A.“__._.._..._ .. __ _ v, 3. I have two lawnmowers, one is electric, the other is gas. Every weekend I decide which lawnmower to use according to the following rules: ' If I used the electric mower last weekend, I will roll two dice. If the sum of the two dice is nine or more, then I will use the electric mower again. Otherwise I‘ll use the gas mower. ' If I used the gas mower last weekend, I will select a card from a deck of 52 playing cards. If I select a face card (Jack, Queen or King) then I will use the electric mower. Otherwise I will use the gas mower. a) Create the transition matrix T for this Markov Chain, taking the states in the order Electric, Gas. ['2 Marks} ,5- . z 3 it 5' r ? E ? w H ' , =1" W.»- s I ,9 "'1 U r.’ :‘r 7" 3’ 3‘ ‘2 ‘I n _. 5.. 43 f / r .. .h _.. . If _ 2 ﬂ? is {few ‘5 : tiff, : i —- a, 5/ is k: I3 ’22- m : P he “‘4‘: 2' «waft: in r. {in I": u a; ,1 .i ,2 b) In the long run, what is the probability that I will use the electric mower? [5 Marks] if” .4” 5 - r . i if . - (luau .. 1-. i i s r Lgmdkgk, M g; ‘M. J .. (PM T r' ur- ‘- t. r Mm“ 5- 53M inn 'v: . . a . D x " x- I x. “r c) The electric mower is very inefficient. When I use it] only get 5 rows of my lawn completed in one session. The gas mower is more efficient and allows me to complete all 8 rows of my lawn in the one session. In the long run, what is the expected number of rows I will be able to mow in one session? (Hint: Let the random variable X denote the number of rows I am able to complete.) [3 Marks] X : “#— Jaw-3,. x 5% 1/04) ...
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McL 151 Assign 5 KEY - [I ME(fr NAME_1 W Math 151 A03&...

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