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Math Help - matrices, breaking down the word problem

  1. #1
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    Lightbulb matrices, breaking down the word problem

    I have no problem working the matrix once i have set things up. I have worked four problems without a glitch and find myself stuck on how to form the equation to work using the Gauss Jordan elimination method


    The problem: A private investment club has $200,000 earmarked for investment in stocks. to arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high risk, medium risk, and low risk. Management estimates that high-risk stocks will have a rate of return of 15%/year, medium 10%/year and low 6%/year. The members have decided that the investment in low-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of $20,000/year on the total investment (assume that all the money available for the investment is invested)

    I had set things up as
    x=high
    y=med
    z=low

    and started my matrix as

    1+1+1=200,000
    .15+.10+.06=20,000
    1-1-1=0

    I worked the problem correctly, only to find out that my answer did not fit into the problem, thus i have started with the wrong matix equation
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  2. #2
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    Quote Originally Posted by cline1687 View Post
    I have no problem working the matrix once i have set things up. I have worked four problems without a glitch and find myself stuck on how to form the equation to work using the Gauss Jordan elimination method


    The problem: A private investment club has $200,000 earmarked for investment in stocks. to arrive at an acceptable overall level of risk, the stocks that management is considering have been classified into three categories: high risk, medium risk, and low risk. Management estimates that high-risk stocks will have a rate of return of 15%/year, medium 10%/year and low 6%/year. The members have decided that the investment in low-risk stocks should be equal to the sum of the investments in the stocks of the other two categories. Determine how much the club should invest in each type of stock if the investment goal is to have a return of $20,000/year on the total investment (assume that all the money available for the investment is invested)

    I had set things up as
    x=high
    y=med
    z=low

    and started my matrix as

    1+1+1=200,000
    .15+.10+.06=20,000
    1-1-1=0
    Here is your problem. This is x- y- z= 0 or x= y+ z. But x is the number of high risk stocks. You said "the investment in low-risk stocks should be equal to the sum of the investments in the stocks of the other two categories". Your final equation should be z= x+y which is the same as x+ y- z= 0 and so your final row is 1+1-1= 0.

    I worked the problem correctly, only to find out that my answer did not fit into the problem, thus i have started with the wrong matix equation
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