Julia Jones wishes to invest her inheritance of $100,000 so that her return on i
ID: 3005743 • Letter: J
Question
Julia Jones wishes to invest her inheritance of $100,000 so that her return on investment is maximized, but she also wishes to keep her risk level relatively low. She has decided to invest her money in any of three possible ways–CDs that pay a guaranteed 8 percent, stocks that have an expected return of 12 percent, and a money market mutual fund that is expected to return 10 percent. She has decided that the total $100,000 will be invested, but any part (or all) of it may be put in any of the three alternatives. Thus, she may have some money invested in all three alternatives. In formulating this as a linear programming problem, define the variables as follows: C = dollars invested in CDs S = dollars invested in stocks M = dollars invested in money market mutual fund. Suppose Julia has assigned the following risk factors to each investment instrument: CDs (C): 1.1; stocks (S): 4.7; money market mutual fund (M): 3.1. If Julia decides that she wants the risk factor for the whole investment to be less than 3.4, how should the necessary constraint be written?
(1.1C + 4.7S + 3.1M)/100000<=3.4
(1.1C + 4.7S + 3.1M)/3<=3.4
1.1C + 4.7S + 3.1M<=3.4
C + S + M<=3.4
(1.1C + 4.7S + 3.1M)/100000<=3.4
(1.1C + 4.7S + 3.1M)/3<=3.4
1.1C + 4.7S + 3.1M<=3.4
C + S + M<=3.4
Explanation / Answer
the objective function would be to maximize the return
=> Z = 8%on CD's + 12% on stocks + 10% on mutual funds
Z = .08C + .12S + .1M
the constrain would be :
$ 100000 will be invested
=> C + S + M <= 100000
Julia has assigned the following risk factors to each investment instrument: CDs (C): 1.1; stocks (S): 4.7; money market mutual fund (M): 3.1
risk factor is included in accordance to the following formula
[sum of (individual risk factor of constraint*the constraint)]/total investment
=> (1.1C + 4.7S + 3.1M)/100000 <= 3.4
so option 1 is correct
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