Problem $4($adapted from Winston, $2004)$: Carrington Oil produces two types of gasoline, gas $1$ and gas

$2,$ from two types of crude oil, crude $1$ and crude $2.$ Gas $1$ is allowed to contain up to $4\%$ impurities, and

gas $2$ is allowed to contain up to $3\%$ impurities. Gas $1$ sells for $$8$ per barrel, whereas gas $2$ sells for $$12$

per barrel. Up to $3,800$ barrels of gas $1$ and up to $4,200$ barrels of gas $2$ can be sold. The cost per barrel

of each crude, availability, and the level of impurities in each crude are as shown in the following table.

Formulate a linear program to maximize profit.