Chapter 3.11, Problem 9P

Explanation of Solution

Objective function:

• Assume the following,
  • Let “${\text{P}}_{\text{j}}$” be the fraction of project “j” that the user invested.
  • Let “${\text{BA}}_{\text{m}}$” be the amount borrowed at time “m”.
  • Let “${\text{CP}}_{\text{m}}$” be the ending cash position at time “m”.
• The objective function to maximize cash on hand after it accounts for cash flows at time “3” is as follows,

$\begin{array}{c}\text{Max}\text{z=(cash}\text{on}\text{hand}\text{for}\text{3}\text{years)(}\text{Fraction}\text{of}\text{project\_1)}\\ \text{+(cash}\text{on}\text{hand}\text{for}\text{3}\text{years)(}\text{Fraction}\text{of}\text{project\_3)}\\ -\text{(cash}\text{on}\text{hand}\text{for}\text{3}\text{years)(}\text{Fraction}\text{of}\text{project\_2)}\\ \text{+(Cash}\text{flow}\text{at}\text{"2}\text{.5")}-\text{(Amount}\text{borrowed}\text{at}\text{"2}\text{.5")}\\ \text{Max z= 5}{\text{.5P}}_{\text{1}}{\text{+6P}}_{\text{3}}-{\text{P}}_{\text{2}}\text{+1}{\text{.03CP}}_{\text{2}\text{.5}}-\text{1}{\text{.035BA}}_{\text{2}\text{.5}}\end{array}$

• The above function subject to the following conditions,
  • “${\text{CP}}_0=2-3{\text{P}}_1-{\text{2P}}_2-2{\text{P}}_{\text{3}}+{\text{BA}}_0$” that denotes ending cash position at time “0”