1. INVESTMENTS PROBLEM
(3.4-11)
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2. PROBLEM
 Al Ferris has $60,000 that he wishes to invest now in order
to use the accumulation for purchasing a retirement
annuity in 5 years.
 After consulting with his financial adviser, he has been
offered four types of fixed-income investments, which we
will label as investments A, B, C, D.
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3. CONSTRAINTS
 Investments C and D will each be available at one time in the
future.
 Each dollar invested in C at the beginning of year 2 returns
$1.90 at the end of year 5.
 Each dollar invested in D at the beginning of year 5 returns
$1.30 at the end of year 5.
 Al wishes to know which investment plan maximizes the
amount of money that can be accumulated by the beginning of
year 6.
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4.  All the functional constraints for this problem can be expressed
as equality constraints.
 To do this, let At, Bt, Ct, and Dt be the amount invested in
investment A, B, C, and D, respectively, at the beginning of year t
for each t where the investment is available and will mature by
the end of year 5.
 Also let Rt be the number of available dollars not invested at the
beginning of year t (and so available for investment in a later
year).
 Thus, the amount invested at the beginning of year t plus Rt must
equal the number of dollars available for investment at that time.
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5. TO DO
 Write such an equation in terms of the relevant variables
above for the beginning of each of the 5 years to obtain the
five functional constraints for this problem.
 Formulate a complete linear programming model for this
problem.
 Solve this model by the simplex model.
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6. ASSUMPTIONS
 At – Amount invested in investment A at the beginning of
the year t.
 Bt – Amount invested in investment B at the beginning of
the year t.
 Ct – Amount invested in investment C at the beginning of
the year t.
 Dt – Amount invested in investment D at the beginning of
the year t.
 Rt – Amount not invested at the beginning of the year t.
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7. EQUATIONS
 Objective function:
Max P= 1.40A1 + 1.70B2 + 1.90C2 + 1.30D5 + Rt
 Subject to
A1+B1+R1=60,000
A2+B2+C2-R1+R2=0
-1.40A1+A3+B3-R2+R3=0
-1.40A2+A4-1.70B1-R3+R4=0
-1.40A3-1.70B2+D5-R4+R5=0
At >= 0 ,Bt > = 0,Ct >= 0,Dt > = 0,Rt >= 0
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A1+B1+R1 =60,000
A2+B2+C2+R2 =R1
A3+B3+R3 =R2+1.40A1
A4-1.70B1+R4 =R3+1.40A2
D5+R5 =R4+1.40A3+1.70B2

8. SOLUTION
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 LINGO