Coding Challenge: Simplex algorithm w/ visualizations

Hey,
Since you made a TSP example, here's another curious optimization problem from the field of linear programming.
Solve this using simplex algorithm:

Suppose we run a bakery and we bake apple, blueberry and pumpkin pies:
1 apple pie requires 1.5 kg of dough, 0.3 cups of sugar and 10 apples
1 blueberry pie requires 3 kg of dough, 0.4 cups of sugar and 3 cups of blueberries
1 pumpkin pie requires 2 kg of dough, 0.1 of sugar and 2 pumpkins

We've got 100 of dough, 7 cups of sugar, 100 apples, 30 cups of blueberries and 10 pumpkins.

Each pie has a price per pie:
Apple pie is $5
Blueberry pie is $6.25
Pumpkin pie is $4

How many pies of each kind we need to produce (maximizing the income)?

Would be cool to see the shape these constraints make in 3D. Everything you need to solve it is on wiki page:
https://en.wikipedia.org/wiki/Simplex_algorithm

Suggest your problems in the comments!