Question

Super Sand Investment Company is deciding on future investments for the coming two years and is considering four bonds. The investment details for the next two years are given in the table below.

	Investment Requirements ($)
	Year 1	Year 2
Bond A	25,000	30,000
Bond B	15,000	21,000
Bond C	8000	9500
Bond D	10,000	7000

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The net worth of these four bonds at maturity is $60,000, $40,000, $25,500, and $18,000, respectively. The firm plans to invest $35,000 and $62,000 in Year 1 and Year 2, respectively. You develop the following binary integer programming model for maximizing the net worth.

Build the model and interpret the results:

Answer 1

Here , the binary integer programming , 0-1 or No-Yes concept ,

We have 4 different Bonds for Investment , A , B , C and D.

X_A = 1 if Bond A is selected , 0 otherwise.

X_B = 1 if Bond B is selected , 0 otherwise.

X_C = 1 if Bond C is selected , 0 otherwise.

X_D = 1 if Bond D is selected , 0 otherwise.

Investment Life span of two years,

	Bond A	Bond B	Bond C	Bond D	Fund
Year 1	25,000	15,000	8000	10,000	$35,000
Year 2	30,000	21,000	9500	7000	$62,000
Return	$60,000	$40,000	$25,500	$18,000

Model as,

Maximize : 60000 X_A + 40000 X_B +25500 X_C​​​​​​​ +18000 X_D​​​​​​​

S.T,

25000 X_A + 15000 X_B​​​​​​​ +8000 X_C​​​​​​​ +10000 X_D​​​​​​​ <= 35000 ( year 1)

30000 X_A + 21000 X_B​​​​​​​ +9500 X_C​​​​​​​ +7000 X_D​​​​​​​ <= 62000 (year 2)

X_i = 0-1

after solving the model with excel solver

Solution vector x:
X_A = 0.0000
X_B​​​​​​​ = 0.0000
X_C​​​​​​​ = 4.3750 ( binary value =1)
X_D​​​​​​​ = 0.0000
Objective function f(x) = 111562.5000.

The company should prefer to invest in bond C ,