Chapter 3, Problem 49RP

Explanation of Solution

LP to find an investment strategy:

• Let “${\text{I}}_{\text{mn}}$” be the amount invested at starting of month “m” for a period of “n” months.
• The Linear Programming (LP) to maximize cash on hand at the beginning of month “5” is given as follows,

$\text{Max z=1}{\text{.08I}}_{\text{14}}+1.03{\text{I}}_{23}+1.01{\text{I}}_{32}+1.001{\text{I}}_{\text{41}}$

• The above function subject to the following conditions,
  • “${\text{I}}_{\text{11}}{\text{+I}}_{\text{12}}{\text{+I}}_{\text{13}}{\text{+I}}_{\text{14}}\text{+600 = 400+400}$” denotes the revenue “400” received by the Finco after which it pays bills “600” at the beginning of month “1”.
  • “${\text{I}}_{\text{21}}{\text{+I}}_{\text{22}}{\text{+I}}_{\text{23}}\text{+500 = 1}{}_{}$