Question

In: Statistics and Probability

Sansuit Investments is deciding on future investments for the coming two years and is considering four...

Sansuit Investments 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.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. Develop and solve a binary integer programming model for maximizing the net worth

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

Solutions

Expert Solution

Answer:

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

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

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

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

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

XD = 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 XA + 40000 XB +25500 XC +18000 XD​​​​​​​

S.T,

25000 XA + 15000 XB​​​​​​​ +8000 XC​​​​​​​ +10000 XD​​​​​​​ <= 35000 ( year 1)

30000 XA + 21000 XB​​​​​​​ +9500 XC​​​​​​​ +7000 XD​​​​​​​ <= 62000 (year 2)

Xi = 0-1

after solving the model with excel solver

Solution vector x:
XA = 0.0000
XB​​​​​​​ = 0.0000
XC​​​​​​​ = 4.3750 ( binary value =1)
XD​​​​​​​ = 0.0000
Objective function f(x) = 111562.5000.

The company should prefer to invest in bond C ,


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