Chapter 3, Problem 61RP

Explanation of Solution

LP to minimize the cost of paying bills on time:

• Let “LT” be the dollars amount borrowed for long-term.
• Let “${\text{ST}}_{\text{m}}$” be the balance that is unpaid in the short term loans at the end of month “m”.
• Let “${\text{CH}}_{\text{m}}$” be the money on hand at the end of month “m”.
• The Linear Programming (LP) to cost of paying bills on time is as follows,

$\text{Min}{\text{z=90LT+40ST}}_1+{\text{40ST}}_2+{\text{40ST}}_3+{\text{40ST}}_4+{\text{40ST}}_5+{\text{40ST}}_6$

• The above function subject to the following conditions,
  • “${\text{LT+ST}}_{\text{1}}{\text{+2=5+CH}}_{\text{1}}$” denotes the cash borrowed for the month July.
  • “${\text{CH}}_{\text{1}}{\text{+ST}}_{\text{2}}{\text{+2=5+CH}}_{\text{2}}\text{+1}{\text{.04ST}}_{\text{1}}$” denotes the cash borrowed for the month August