An Investment Problem A portfolio manager has

$100K

to invest, in three kinds of securities: (a) a utilities stock paying

8%

dividend, (b) a software stock paying

3%

dividend, (c) a bond paying

5%

interest. Not all of the amount need to be invested. Further, there are the following restrictions. Amount invested in bonds need to be at least two times the amount invested in stocks. At least

$30K

need to be invested in bonds, and no more than

$60K

can be in the utilities stock. What investment policy must be pursued to maximize the return?\ (a) Set up the problem as an LP. Clearly define decision variables.\

a>=0,b>=0,c>=0,a= amoint in utility stock \ a+b+c=2(a+b),c= arront in bond \ -c=30,000\ -c+2a+2b

\

c>=30.000\ a+b

\ (b) Express your LP in Standard form (SF).\

Max z=0.08a+0.036+0.05c,\ a+b+c

\

a>=0,b>=0,c>=0

\ (c) Express your LP in Canonical form (CF).\ (d) Express your LP in matrix form with either

or

=

for the constraints.\

Express your LP in matrix form with either =vec(0)\ Is investing $35K in utilities stock, $50K in bonds and $10K in the soft

\ (e) Is investing

$35K

in utilities stock,

$50K

in bonds and

$10K

in the software stock a feasible solution? If so, optimal solution to the LP?\ No, the following investmen strategy will not be feasible solution be cause it does not satisfy the constraint the invested in bonds will be two thres the amont invested in stoeles.\ (f) Is investing

$10K

in utilities stock,

$70K

in bonds and

$10K

in the software stock a feasible solution? optimal solution to the LP?\ Yes, the following imestrent strategy will be a feasibe solution because it satisfies all of the given but it is not on optional soluten because the objetic function is not maximized

An Investment Problem A portfolio manager has $100K to invest, in three kinds of securities: (a) a utilities stock paying 8% dividend, (b) a software stock paying 3% dividend, (c) a bond paying 5% interest. Not all of the amount need to be invested. Further, there are the following restrictions. Amount invested in bonds need to be at least two times the amount invested in stocks. At least $30K need to be invested in bonds, and no more than $60K can be in the utilities stock. What investment policy must be pursued to maximize the return? (a) Set up the problem as an LP. Clearly define decision variables. a0,b0,c0a+b+c100,000c2(a+b)c30,000a=amointinutilitystrckb=amointinsotharestockc=ambantinbondMaxz=0.08a+0.03b+0.05c c30,000 c+2a+2b0 (b) Express your LP in Standard form (SF). Maxz=0.08a+0.03b+0.05ca+b+c100,000c2(a+b)c30,000a+b60,000a0,b0,c0a+b+c100,0002a+2bc0c30,000a+b60,000 (c) Express your LP in Canonical form (CF). (d) Express your LP in matrix form with either or = for the constraints. (e) Is investing $35K in utilities stock, $50K in bonds and $10K in the software stock a feasible solution? If so, optimal solution to the LP? No, the following investment shategy will not be feasible solution be cause it does not satisfy the constraint the invested in bonds will be two times the amount invested in stocks. (f) Is investing $10K in utilities stock, $70K in bonds and $10K in the software stock a feasible solution? If optimal solution to the LP? Kes, the following investment strategy will be a feasible solution because it satisfies all of the given but it is not on optional solutien because the obiectic function is not maximized