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Investment problem

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Investment problem

  1. 1. INVESTMENTS PROBLEM (3.4-11) 1 9/3/2012
  2. 2. PROBLEM 2 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. 9/3/2012
  3. 3. CONSTRAINTS 3 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. 9/3/2012
  4. 4. 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. 9/3/2012
  5. 5. TO DO 5 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. 9/3/2012
  6. 6. ASSUMPTIONS 6 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. 9/3/2012
  7. 7. EQUATIONS 7 Objective function: Max P= 1.40A1 + 1.70B2 + 1.90C2 + 1.30D5 + Rt Subject to A1+B1+R1=60,000 A1+B1+R1 =60,000 A2+B2+C2-R1+R2=0 A2+B2+C2+R2 =R1 -1.40A1+A3+B3-R2+R3=0 A3+B3+R3 =R2+1.40A1 -1.40A2+A4-1.70B1-R3+R4=0 A4-1.70B1+R4 =R3+1.40A2 -1.40A3-1.70B2+D5-R4+R5=0 D5+R5 =R4+1.40A3+1.70B2At >= 0 ,Bt > = 0,Ct >= 0,Dt > = 0,Rt >= 0 9/3/2012
  8. 8. SOLUTION 8 LINGO 9/3/2012

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