Linear Programming Problem
I have a problem for you. Here is a description. I have raw material (cocoa beans) from which I get 1 ton of cocoa liquor per hour. The price of cocoa liquor is let say 3.300 USD/ton. From 1 ton of cocoa liquor I can produce 0.35 ton of cocoa butter and 0.48 ton of cocoa powder. The price of butter is let say 5.000 USD/ton and the price of powder is lets say 1.200 USD/ton.
cocoa liquor (1 ton, 3300 USD/ton)->cocoa butter(0.35 ton, 5000 USD/ton)
->cocoa powder(0.48 ton, 1200 USD/ton)
The ratio between cocoa butter and cocoa powder is fixed. Cocoa liquor can be sold as independent product as it is or it can be further processed into cocoa butter and cocoa powder. The question now is, how much cocoa liquor should I sell as independant product and how much cocoa liquor should I further process into cocoa butter and cocoa powder to maximize the profit? How should I deal with this? Please help!