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Math Help - Could someone check my answer or tell me what im doing wrong? "Quant. Methods"

  1. #1
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    Could someone check my answer or tell me what im doing wrong? "Quant. Methods"

    Im not sure if this is right but I was wondiering if someone who knew a little more about quantitive methods could help me figure this out tell me if its right or wrong. Its a Decision Analysis problem.
    Thanks

    Dollar Department Stores has the opportunity of acquiring either 3, 5, or 10 leases from the bankrupt Granite Variety Store chain. Dollar estimates the profit potential of the leases depends on the state of the economy over the next five years. There are four possible states of the economy as modeled by Dollar Department Stores, and its president estimates P(s1) = .4, P(s2) = .3, P(s3) = .1, and P(s4) = .2. The utility has also been estimated. Given the payoffs (in $1,000,000's) and utility values below, which decision should Dollar make using expected utility as its decision criterion?

    Payoff Table

    State Of The Economy
    Over The Next 5 Years
    Decision s1 s2 s3 s4
    _________________________
    d1 -- buy 10 leases | 10 | 5 | 0 | -20 |
    d2 -- buy 5 leases | 5 | 0 | -1 | -10 |
    d3 -- buy 3 leases | 2 | 1 | 0 | - 1 |
    d4 -- do not buy | 0 | 0 | 0 | 0 |

    Utility Table

    Payoff (in millions)------ +10 +5 +2 +1 0 -1 -10 -20
    Utility -------------- +10 +5 +2 +1 0 -1 -20 -50


    MY ANSWER---
    D1=10(.4)+5(.3)+(0(.1)+-20(.2)=1.5
    D2=5(.4)+0(.3)+-1(.1)+-10(.2)=-.1
    D3=2(.4)+1(.3)+0(.1)+-1(.2)=.9
    D4=0

    Dollar should pick d2
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by jwells1999 View Post
    Im not sure if this is right but I was wondiering if someone who knew a little more about quantitive methods could help me figure this out tell me if its right or wrong. Its a Decision Analysis problem.
    Thanks

    Dollar Department Stores has the opportunity of acquiring either 3, 5, or 10 leases from the bankrupt Granite Variety Store chain. Dollar estimates the profit potential of the leases depends on the state of the economy over the next five years. There are four possible states of the economy as modeled by Dollar Department Stores, and its president estimates P(s1) = .4, P(s2) = .3, P(s3) = .1, and P(s4) = .2. The utility has also been estimated. Given the payoffs (in $1,000,000's) and utility values below, which decision should Dollar make using expected utility as its decision criterion?

    Payoff Table

    State Of The Economy
    Over The Next 5 Years
    Decision s1 s2 s3 s4
    _________________________
    d1 -- buy 10 leases | 10 | 5 | 0 | -20 |
    d2 -- buy 5 leases | 5 | 0 | -1 | -10 |
    d3 -- buy 3 leases | 2 | 1 | 0 | - 1 |
    d4 -- do not buy | 0 | 0 | 0 | 0 |

    Utility Table

    Payoff (in millions)------ +10 +5 +2 +1 0 -1 -10 -20
    Utility -------------- +10 +5 +2 +1 0 -1 -20 -50


    MY ANSWER---
    D1=10(.4)+5(.3)+(0(.1)+-20(.2)=1.5
    D2=5(.4)+0(.3)+-1(.1)+-10(.2)=-.1
    D3=2(.4)+1(.3)+0(.1)+-1(.2)=.9
    D4=0

    Dollar should pick d2
    I find it difficult to follow what you have done, but should you not be maximising utility? Form what you write it looks like you have minimised it.

    RonL
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