Hello, Brazuca!
2) Each gallon of garlic dressing requires 2qt oil and 2qt vinegar.
Each gallon of tofu dressing requires 3qt oil and 1qt vinegar.
Jim makes $3 profit on each gallon of garlic dressing
. . and $2 profit on each gallon of tofu dressing.
He has 18qt oil and 10qt vinegar on hand.
How many gallons of each type of dressing should he make to maximize profit?
Tabulate the given information.
Let = number of gallons of Garlic dressing: .
Let = number of gallons of Tofu dressing: .
From [1] and [2], the region is in Quadrant 1.
Graph the line of [3]: .
It has intercepts and
Draw the line and shade the region below the line.
Graph the line of[4]: .
It has intercepts and
Draw the line and shade the region below the line.
The shaded region looks like this: Code:

10 *
 *
 *
6 o *
::::o *
:::::::::o
:::::::::::* o
 +       *   o  
 5 9
The critical points are the vertices of this region.
We know three of them: .
The fourth is the intersection of the lines of [3] and [4].
Solve the system and we get: .
Test these vertices in the profit function,
. . to determine which produces maximum profit.