Can anyone help me figure out how to maximise this problem knowing that the constraint is a leontief function?
$$ \max_{WS,W,S}\pi_{WS} = p_{WS}.WS - (p_W . W + p_S.S)\\ \text{subject to } WS = \min\left(\frac{S}{a_S}; \frac{W}{a_W} \right) $$
I dropped the subscripts to facilitate the example. "p" refers to prices, while "a" refers to the constants of the leontief function. In this example, I'm interested in obtaining a composite input WS using Water (W) and Land (S). The choice of the leontief function is simply because the two inputs are complementary, and not substitutes, they are also essential to the production process.