\(\text{let }n_c \text{ be the number of cups of lemonade sold and }\\n_b \text{ be the number of lemon bars sold.}\)
\(\text{we have 3 constraints }\\ 2\cdot n_c + 1.5 \cdot n_b \geq 500 \\ 0.25 n_c + 0.2 n_b \leq 100\\ n_c \geq 150\)
Oh oops, I missed that they called nc = x and nb = 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.