Chapter 3.11, Problem 4P

Explanation of Solution

Formulation of Linear Programming (LP):

• Assume the following,
  • Let “${\text{A}}_{\text{j}}$” be the units of bond “j” bought at ask price.
  • Let “${\text{B}}_{\text{j}}$”be the units of bond “j” sold at bid price.
  • Let “${\text{C}}_{\text{y}}$” be the cash on hand after year “y” payments are received.
• The Linear Programming (LP) is formulated to maximize net profit from buying and selling bonds as follows,

$\text{z=}980{\text{B}}_1{\text{+970B}}_2+960{\text{B}}_3+940{\text{B}}_4-990{\text{A}}_1-985{\text{A}}_2-972{\text{A}}_3-954{\text{A}}_4$

• The above function is subject to the following conditions,
  • All variables >= “0”.
  • “${\text{C}}_1\text{=}100({\text{A}}_1-{\text{B}}_1)+80({\text{A}}_2-{\text{B}}_2)+70({\text{A}}_3-{\text{B}}_3)+60({\text{A}}_4-{\text{B}}_4)$” that denotes cash on hand after year “1” payments are received

Explanation of Solution

Reasons:

• As the users wish to sell all the bonds, the users limited the number of quantities of bonds that can be sold...