Solving the Whole Simplex

At Mappy we sell 3 different subscriptions to our app:

• Basic – $30/mo.
• Pro – $60/mo.
• Enterprise – $120/mo.

Due to the number of external API licenses that we hold, we have the following constraints:

• We can sell no more than 100 basic subscriptions each month.
• We can sell no more than 25 pro subscriptions each month.
• We can sell no more than 10 enterprise subscriptions each month.
• We have only 150 API keys available each month. A basic subscription uses 1, a pro subscription uses 2, and an enterprise subscription uses 3.

We'll be using our simplex solver to help answer the question:

How many of each subscription should we sell to maximize profit?

Implement the solve method. It assumes a SimplexSolver has been constructed and the constraints have been added. Its job is to add the slack variables and pivot until the tableau is in its optimal solved state.

Once this is working, we'll finally have a program that can answer our original question (and any other optimization problems the business has in the future)!

1. Call the add_slack_variables method.
2. While the tableau should pivot:
   1. Get the pivot column.
   2. Get the pivot row.
   3. Pivot the tableau.