Harrison and Lara have discovered a counterfeit jewelry operation. Two workers, Choot and Wanlah, sell fake "gold" watches and "diamond" rings for a notoriously frugal mob boss. They need to gather intel and file a report on their discovery.

Question

The adventurers learn that the mob boss demands a minimum of 12 watches and 30 rings to be sold every day, and has figured out how to get what he wants while paying his two workers the least possible amount (while still honouring their agreed-upon hourly wages). While Lara and Harrison can't tell how many hours each worker spends selling the jewelry, or how many items they actually sell each day.

what is the optimization equation?

Answer 1

The optimization equation in this scenario can be formulated to minimize the cost while meeting the minimum sales requirements set by the mob boss.

Let's assume that Choot and Wanlah are paid hourly wages of C dollars and W dollars respectively. Additionally, let the number of hours Choot and Wanlah work be denoted as x and y respectively.

The cost function (C) can be calculated as follows:
C = C * x + W * y

To meet the minimum sales requirements, we can set up the following constraints:
12 watches <= x
30 rings <= y

Therefore, the optimization equation becomes:
Minimize C = C * x + W * y
subject to the constraints:
12 watches <= x
30 rings <= y

In this equation, the aim is to minimize the cost (C) while ensuring that the number of watches (x) and rings (y) sold meets or exceeds the minimum requirements.