No, this would not be a linear function. Being linear means it creates a straight line, but this function has an x squared. Anytime x^2 is in a function, the graph is a u shape, called a parabola. A simple linear function is y=x :D
The second constraint is the same as the objective function, so your problem boils down to finding integer solutions to
.. 3x1 +5x2 = 36
There are 3 solutions. They are (x1, x2) = (12, 0), (7, 3), (2, 6)
The value of the objective function there is (obviously) 36.
Get running mate I believe you may have heart disease in the near future but good luck and try not to eat any more people