GEOMETRY ​

$\text{let }n_c \text{ be the number of cups of lemonade sold and }\\n_b \text{ be the number of lemon bars sold.}$

$\text{we have 3 constraints }\\ 2\cdot n_c + 1.5 \cdot n_b \geq 500 \\ 0.25 n_c + 0.2 n_b \leq 100\\ n_c \geq 150$

Oh oops, I missed that they called n_c = x and n_b = y, oh well you'll figure it out.

I don't see any solution method any better than just plugging in the points and checking.

so every pair but the first listed is acceptable.