You sell homemade hot chocolate, which only needs two ingredients: milk and cocoa powder. The production function is given by(,)=(min{,})

1

2

,where

represents cups of milk,

represents tablespoons of cocoa powder and

represents cups of hot chocolate. One cup of milk costs 40 cents and one tablespoon of cocoa powder costs 10 cents. It is a perfectly competitive market with each cup of hot chocolate sold at $4. Solve for the optimal cups of hot chocolate that you should make to maximize profit.

*=?