Chapter 3, Problem 45RP

Explanation of Solution

Amount of stocks to be sold:

• Assume the following,
  • Let “${\text{SH}}_{\text{j}}$” be the shares of stock “j” sold.
  • Let “${\text{L}}_{\text{j}}$” be the shares of stock “j” left.
  • Let “Tax” be the amount that is paid in tax.
  • Let “Tc” be the amount which is paid in transaction costs.
• The objective function to maximize the expected value is as follows,

${\text{Max z=36L}}_{\text{1}}+39{\text{L}}_2+42{\text{L}}_3+45{\text{L}}_4+51{\text{L}}_5+55{\text{L}}_6+63{\text{L}}_7+64{\text{L}}_8+66{\text{L}}_9+70{\text{L}}_{\text{10}}$

• The above function subject to the following conditions,
  • $\begin{array}{l}{\text{30SH}}_1+34{\text{SH}}_2+43{\text{SH}}_3+47{\text{SH}}_4+49{\text{SH}}_5+53{\text{SH}}_6\\ +60{\text{SH}}_7+62{\text{SH}}_8+64{\text{SH}}_9+66{\text{SH}}_{10}-\text{Tax}-\text{Tc}=30000\end{array}$
    • This function denotes the amount that must be left, after taxes and transaction costs.
  • “${\text{SH}}_{\text{j}}{\text{+L}}_{\text{j}}\text{=100}$”  for “$\text{j=1,2,}\mathrm{}$