Cass Investment Co. (CIC), must decide how much to invest in a number of alterna
ID: 420554 • Letter: C
Question
Cass Investment Co. (CIC), must decide how much to invest in a number of alternative investment opportunities, which are summarized below:
Investment Opportunity
Country
Expected Return (%)
Maximum Investment ($million)
A
US
9
2
B
Japan
10
12
C
Canada
8
8
D
US
7
6
E
Kuwait
7
10
F
US
6
4
G
US
11
9
Company policy requires that the total amount invested inside the US should be at least as much as invested outside the US. In addition, the total amount invested in North America, at most 30% should be invested in Canada.
CIC has $30 million to invest and obviously wants to maximize its total expected return on investment.
REQUIREMENTS:
Formulate the problem into a linear programming problem. Clearly definethe objective function and decision variables and identify the constraints.
Solve the LP problem using Excel Solver. Copy and paste Excel output below.
3.Present a layman’s interpretation (report) of the solution obtained in part 2. Be sure your interpretation is clear, complete and concise. In other words, list how much will be invested in each of the 7 investment opportunities, how much will be the optimum return on the portfolio, etc.
Investment Opportunity
Country
Expected Return (%)
Maximum Investment ($million)
A
US
9
2
B
Japan
10
12
C
Canada
8
8
D
US
7
6
E
Kuwait
7
10
F
US
6
4
G
US
11
9
Explanation / Answer
Answer : The problem can be solved using a ixed integer linear program
Let X i =0 or 1 where i= {A,B,C,D,E,F,G}
If X i =1 it means the project is selected for investment , if X i=0 means project is not selected for investment.
Also if X i=1 then return of investment = 1*Expected return in % i *Investment i
The objective function can be stated as below:
Maximize [XA*0.09 *2 +XB *0.1*12 +XC*0.08*8+ XD*0.07*6+ XE*0.07*10 + XF*0.06*4 +XG*0.11*9 ]
Maximize [XA*0.18 + XB*1.2 + XC*0.64 +XD*0.42 +XE*0.7 +XF*.24+XG*0.99 ]
Constraints:
XA*2+XB*12+XC*8+XD*6+XE*10+XF*4+XG*9 <= 30........................(1)
XA*2+XD*6+XF*4+XG*9 >= XB*12+XC*8+XE*10 ............................(2)
XC*8 >= 0.3( XA*2+XD*6+XF*4+XG*9 )
XC*8 >= XA*0.6+XD*1.8+XF*1.2+XG*2.7....................................(3)
The above objective functions and constraints can be run and the values of Xi for i={A,B,C,D,E,F,G}
can be obtained.
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