3. (25 points) Investor Sandy Smith has $10,000 to invest in four projects. The

Question

3. (25 points) Investor Sandy Smith has $10,000 to invest in four projects. The following table gives the cash flow for the four investments: PROJECT Cash Flow ($1000) at the start of YEAR 1.00 YEAR 2 0.50 0.60 1.00 0.40 YEAR 3 0.30 0.20 0.80 0.60 YEAR 4 1.80 1.50 1.90 1.80 YEAR 1.20 1.30 0.80 0.95 3 4 The information in the table can be interpreted as follows: For project 1, $1.00 invested at the start of year 1 will yield $0.50 at the start of year 2, S0.30 at the start of year 3, $1.80 at the start of year 4, and $1.20 at the start of year 5. The other rows may be interpreted in a similar manner. The entry 0.00 indicates that no transaction is taking place. Smith has the additional option of investing in a bank account that earns 6.5% annually. All Funds accumulated at the end of 1 year can be reinvested in the following year. Formulate the problem as a linear program to determine the best allocation of funds. Make sure you define all the decision variables. 0.00

Explanation / Answer

Let Xi is the dollar invested in projects i i=1,2,3,4

Yj= dollar invested in bank in year j j - 1,2,3,4,5

We need to maximize the amount we get in year 5 i.e. Y5

Maximize Z = Y5

Subject to

X1+X2+0X3+X4+Y1<= $10000

( this shows the total investment in projects and banks in year 1 should be less than or equal to $10000)

The first-year return should be the funds in hand for year 2

0.5X1+0.6X2-X3+0.4X4+1.065Y1= Y2 (6.5% return on bank investment expressed as 1.065)

Similarly for other years

0.3X1+0.2X2+0.8X3+0.6X4+1.065Y2=Y3

1.8X1+1.5X2+1.9X3+1.8X4+1.065Y3=Y4

1.2X1+1.3X2+0.8X3+0.95X4+1.065Y4= Y5

All variables >=0

please free to comment if u have any doubt thanks

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