Question

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.

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	Investment Requirements ($)
	Year 1	Year 2
Bond A	25,000	30,000
Bond B	15,000	21,000
Bond C	8,000	9,500
Bond D	10,000	7,000

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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. Develop ( write all the constraints) and solve a binary integer programming model with SOLVER for maximizing the net worth. Give your answer clearly

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.

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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