I would like to create a rectangular vegetable patch. The fencing for the east and west sides cost $6 per foot, and the fencing for the north and south sides cost only $3 per foot. I have a budget of $96 for the project. What are the dimensions of the vegetable patch with the largest area I can enclose? (Let the variable x denote the length of the south and north side of the garden in feet. Let the variable y denote the length of the east and west sides of the garden in feet).

- Find the objective function( The area of the garden which has to maximize), Find the constraint(Cost of the fence), solve the optimization problem for x and y, and what is the largest area