My attempt at lagrange has gotten me no where:

f(x,y) = x * (5+y)

g(x,y) = 300(x/1000) + 500y

F(x,y) = f(x,y) - lambda(g(x,y) - k)

F(x, y, lambda) = x * (5 + y) - lambda(300/1000x + 500y - k)

F(x, y, lambda) = 5x + xy - 3/10 lambda x - 500 lambda y + lambda k

Fx = 5 + y - 3/10 lambda - 500y = 0

Fy = x - 500 lambda = 0

Flambda = -3/10x - 500y + k = 0