An investor has $10.000 available for investment. He has instructed his investme

Question

An investor has $10.000 available for investment. He has instructed his investment firm that his money be invested in three stocks, A, B, C, so that no more than $5000 is invested in any one stock but at least $1,000 is invested in each stock. Since lie perceives stock A to have the highest potential for appreciation but also the highest risk, he wants to have invested in that stock an amount that does not exceed the combined amount invested in the other two stocks. In addition, he wants the firm to use its current data and invest in a manner that maximizes the expected overall gain during a one-year period. The stocks, the current price per share, and the firm's projected stock price a year from now arc summarized in the following table: Formulate a linear programming model for the investment company (define variables and write the objective function and constraints).

Explanation / Answer

DECISION VARIABLES:

Let x be the investment in the stock A
Let y be the investment in the stock B
Let z be the investment in the stock C

According to given table,
A gives return of $30 -$20 =$10 after one year
B gives return of $60 -$50 =$10 after one year
C gives return of $125 -$100 =$25 after one year

OBJECTIVE:
Our objective is to maximize overall gain. So,
Max 10*x + 10*y + 25*z

CONSTRAINTS:
subject to
Constraint 1: Upper Bound on investment in stock A
So,  x  <= y+z ...............(1)

Constraint 2: budget constraint
 x +y +z <= 10000............... (2)

Constraints: Bounds

1000<=x <=5000  .....................(3)
1000<=y <=5000 .....................(4)
1000<=z <=5000  .....................(5)

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