Chapter 3.11, Problem 3P

Explanation of Solution

Formulation of Linear Programming (LP):

• Assume the following,
  • Let “AI” be the dollars invested in investment “A”.
  • Let “BI” be the dollars invested in investment “B”.
  • Let “${\text{C}}_{\text{0}}$” be the leftover cash at time “0”.
  • Let “${\text{C}}_1$” be the leftover cash at time “1”.
  • Let “${\text{C}}_2$” be the leftover cash at time “2”.
• The Linear Programming (LP) is formulated to maximize the cash on hand at time “3” as follows,

$\begin{array}{l}\text{z=}\text{Leftover cash at time "2"}\text{+Dollars invested in investment "B"}\\ \text{z=}{\text{C}}_{\text{2}}\text{+1}\text{.9B}\end{array}$

• The above function is subject to the following conditions,
  • All variables >= “0”

Explanation of Solution

“Yes”, the user can guess the optimal solution to this LP problem.

Optimal solution:

• The best solution to this LP is,
  • “${\text{BI= C}}_0\text{ = \$10000}$”
  • “${\text{AI}}_{}$