Chapter 3.11, Problem 8P

Explanation of Solution

Linear Programming (LP) to determine the monthly payment:

• Assume the following,
  • Let “${\text{SB}}_{\text{m}}$” be the ending month “m” Saks balance.
  • Let “${\text{BB}}_{\text{m}}$” be the ending month “m” Bloomingdale’s balance.
  • Let “${\text{MB}}_{\text{m}}$” be the ending month “m” Macy’s balance.
  • Let “${\text{SP}}_{\text{m}}$” be the month “m” Saks payment.
  • Let “${\text{BP}}_{\text{m}}$” be the month “m” Bloomingdale’s payment.
  • Let “${\text{MP}}_{\text{m}}$” be the month “m” Macy’s payment.
• The LP is formulated to minimize the total of all Madonna’s payments as follows,

$\text{Min z= }{\displaystyle {\sum }_{m-1}^{m-36}({\text{SP}}_{\text{m}}+{\text{BP}}_{\text{m}}}+{\text{MP}}_{\text{m}})$

• The above function subject to the following conditions,
  • “${\text{BP}}_{\text{m}}{\text{+SP}}_{\text{m}}{\text{+MP}}_{\text{m}}\le 5000$” for “$\text{m=1,}\text{2,}\text{3}\text{,}\mathrm{....}36$” and this denotes budget condition that Madonna’s willing to allocate up to $5000 per month to pay off the credit cards.
  • “${\text{SB}}_0\text{=20000}$” that demotes the amount at Saks fifth avenue