The question is: What quantities does the manager control? What can the manager manipulate to influence profit? It is incomplete simply to say that the manager controls the amount of each final product to make. The manager controls, and must determine, how to make each final product and how much to make.

This can be expressed by letting xij $=$ number of barrels of raw gas $$i$=(1,2,3,4)$ used per day to make final product $$j$=($R$,$ P$)$ be the decision variables.

Each barrel of raw gas i that is blended in final product j and then sold generates a profit equal to its selling price minus its cost.

$1)$

Formulate the objective function for this problem.