The region describes a rectangle. F(x,y) is optimized at the intersecting points around the rectangle. You can try plugging in (-3,-5) , (-3,4), (4,4) , (4,-5) and see which one gives you the largest value.
The max value of f(x,y) is at point (4,-5) ---> 4(4) - 7(-5) = 16 + 35 = 51
