Reconsider the Welte Mutual Funds problem from Section 9.2. Define your decision variables variables as the fraction of funds invested invested in each security. security. Also, modify the constraint constraintss limitin investments in the oil and steel industries as follo!s" #o more than $%& of the total funds invested in stoc' (oil and steel) may be invested in the oil industry, and no more than $%& of the funds invested in stoc' (oil and steel) may be invested in the steel industry. a. Solve the revised linear prorammin model. What fraction of the portfolio should be invested in each type of security* b. +o! much should be invested in each type of security* c. What are the total earnins for the portfolio* d. What is the marinal rate of return on the portfolio* hat is, ho! much more could be earned by investin one more dollar in the portfolio*
SOLUTION
a.
-et -et each each dec decis isio ion n vari variab able le,, A, , M, M, + and and /, /, repr repres esent ent the the frac fracti tion on or or pro propo port rtio ion n of the total investment placed in each investment alternative.
Ma0 s.t.
.%1A
3 .4%
A .$ .$A 8.$A
3 3 8
8.5A
3
3 .%56 M
3 .$ 8 .$ 3 8 .6
M .$M .$ M .2 $ M
3 .%1$+
3 .%6$/
3 + 8 .$+ 3 .$+ 8 .2$+
3
Solution" ;b
Atlantic ;il
7 % .41=
acific ;il
7 % .25 1
Mid!est ;il
7 % .%%%
+uber Steel
7 % .6 6 6
/ove /overrnm nmen entt >ond >ondss
7 %.44 %.444 4
/
7 3 / : : A, , M, +, / %
4 % % % %
b.
For a total investment of ?4%%,%%%, !e sho!
Atlantic ;il
7 ?41,=%%
acific ;il
7
25,1%%
Mid!est ;il
7
%.%%%
+uber Steel
7
66,6%%
/overnment >onds
7
44,4%%
otal
?4%%,%%%
c.
otal earnins 7 ?4%%,%%% (.%19) 7 ?1,9%%
d.
Marinal rate of return is .%19
