I'm very new at linear programming and I'm trying to figure out a way to approach this problem below:
You are a CFA (chartered financial analyst). Madonna has come to you because she needs help paying off her credit card bills. She owes the amounts on her credit cards shown in the table below. Madonna is willing to allocate up to $5,000 per month to pay off these credit cards. All cards must be paid off within 36 months. Madonna’s goal is to minimize the total of all her payments. To solve this problem, you must understand how interest on a loan works. To illustrate, suppose Madonna pays $5,000 on Saks during month 1. Then her Saks balance at the beginning of month 2 is 20,000 - (5,000 - 0.005(20,000)) This follows because during month 1 Madonna incurs .005(20,000) in interest charges on her Saks card. Help Madonna solve her problems!
Since this is a multi-period problem, I'm having a bit of difficulty finding a way to model it. I would guess that the decision variables are as follows:
$S_i = $ Amount spent at Saks Fifth Avenue during month $i$
$B_i = $ Amount spent at Bloomingdale's during month $i$
$M_i = $ Amount spent at Macy's during month $i$
$i = 1,2,3,...,36$
However, I am not sure where to go from here (or even if my choice of decision variables will work as chosen.) I would appreciate some advice. Thanks!