Would you like to help me solve this optimisation problem?
$$ \max_{Y_j,A_j,B_j}\pi_j = p_j Y_j - (p_a A_j + p_bB_j)\\ \text{subject to } Y_j = \min\left(\frac{A_j}{\alpha_a}; \frac{B_j}{\beta_b} \right) $$
As you can see above, I'm trying to maximise Y, but the tricky bit is that the constraint is a Leontief function.
In this example, I'm supposed to find the optimal quantities of A_j and B_j as inputs to maximise the quantity of the output Y_j, . alpha and beta are the coefficients of the leontief function.
As much as I'd like an answer, I hope you can teach me the trick to find the solution, not just give a direct solution. Thank you so much
Does anyone know how to do symbolic solving of optimisation problems on maple? I have it but I don't know how to use it for optimisation problems specifically.