# In August 2011, Bank of Hawaii (BOH) stock cost \$45 per share, yielded 4% per year in dividends, and had a risk index of 3.0 per share, while JPMorgan Chase (JPM) stock cost \$40 per share, yielded 2.5% per year in dividends, and had a risk index of 2.0 per share.† You have up to \$25,000 to invest in these stocks, and would like to earn at least \$796 in dividends over the course of a year. (Assume the dividends to be unchanged for the year.) How many shares (to the nearest tenth of a unit) of each stock should you purchase to meet your requirements and minimize the total risk index for your portfolio?

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In August 2011, Bank of Hawaii (BOH) stock cost \$45 per share, yielded 4% per year in dividends, and had a risk index of 3.0 per share, while JPMorgan Chase (JPM) stock cost \$40 per share, yielded 2.5% per year in dividends, and had a risk index of 2.0 per share.† You have up to \$25,000 to invest in these stocks, and would like to earn at least \$796 in dividends over the course of a year. (Assume the dividends to be unchanged for the year.) How many shares (to the nearest tenth of a unit) of each stock should you purchase to meet your requirements and minimize the total risk index for your portfolio?

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Step 1

Let the number of shares of BOH in protfolio be x

the number of shares of JPM in portfolio be y

BOH Stock cost per share = \$45

JPM stock cost per share = \$40

The total amount can be invested is up to 25000. So we say

45x+40y ≤ 25000

Yield on BOH shares  is 4% per year and yield on JPM shares is 2.5% and we need at least the dividend to be \$796 per year.

Dividends on BOH shares = 45x*4.0% = 45*0.04*x=1.8x

Dividends on JPM shares = 40y*2.5% = 40*0.025*y = y

Total dividends = 1.8x+y and we know at least dividends should be \$796 . So

1.8x + y ≥ 796

We need to minimise the Total Risk index. Risk index of BOH is 3 per share and risk index of JPM is 2 per share.

Total risk Index R = 3x+2y

Step 2

Here we need to minimise the Total risk index keeping the constraints in mind. We need to invest enough amount in BOH shares and remaining in JPM shares, such that we get dividends of 796 per year.

We know we can invest upto 25000 and So we invest just enoug money in BOH ...

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