# A value proposition solution

\$24.99

Original Work ?

## Description

5/5 - (1 vote)

Your friend Michael has just been given a gift certificate to use at the latest consolidated
merchandise website, SellU. The distinctive feature of SellU is that it does not tell you
a price until you put together a complete shopping cart. This is because it is really
just forwarding your order to various other suppliers, and it tries to make gains by
combining shipping, using discounts etc.
Michael’s experimentation with the site has revealed that its prices are consistent in the
sense that if you add items to a shopping cart then the price always increases, and if
you remove items it always decreases, but except for that single constraint there seems
to be no observable rhyme or reason for the total prices announced.
Having a certain amount to spend, and a list of items which he might buy, Michael
wants to optimise his purchase. Each item for him has a certain intrinsic value, so he
wants to find a shopping cart that he can afford such that the value (to him) of the items
it contains is as large as possible (Michael, somewhat more rational than the site, thinks
that the value of a collection of items is equal to the sum of their individual values). He
can buy at most one of each type of item (that’s a condition of the gift card). Hours of
fiddling about later, he wonders if there is any good way to find his perfect bundle of
items.