Question

Larry Bird’s Investments needs to develop an investment portfolio for Mrs. Jaimeson from the following list of possible investments. Exactly one of each type of investment is available, and no fractional investments are allowed.

Investment	Cost	Expected Return
A	$6,000	$300
B	$10,000	$1,200
C	$5,500	$280
D	$7,400	$400
E	$2,600	$150
F	$7,000	$390
G	$7,200	$430

      Mrs. Jaimeson has a total of $30,000 to invest. The following conditions must be met: (1) If investment F is chosen, then investment E must also be part of the portfolio, (2) investment A and investment G must either both be chosen or both not be chosen, and (3) of investments B and G, exactly one must be included.

      Formulate this as a mathematical program to determine which stocks should be included in Mrs. Jaimeson’s portfolio to maximize expected return (write out the formulation), and solve it on a computer.

Be sure to define your decision variables clearly for each problem. “Formulate” means to write or type out the decision variable definitions, objective function, and constraints

Answer 1

Formulation:

Let,

Decision variables:

Let i = 1 if the project I is selected otherwise I = 0

i = A, B, C, D, E, F, G for the projects respectively

Objective Function:

Objective is to maximize the expected return:

Max Z = $300A + $1200B + $280C + $400D + $150E + $390F + $430G

Subject to:

(1) Budget available:

$6000*A + $10,000*B + $5,500*C + $7,400*D + $2,600*E + $7,000*F + $7,200*G <= $30,000

(2) If investment F is chosen, then investment E must also be part of the portfolio,

F <= E or F – E <= 0

(3) investment A and investment G must either both be chosen or both not be chosen,

A = G or A - G = 0

(4) of investments B and G, exactly one must be included.

B + G <= 1

(5), all the variable i are binary variables

Excel model:

Optimal Solution:

Select projects – B, D, E, F

Total expected return - $2140