A firm’s production function is given by 

Q = 80KL
which is subject to a budgetary constraint, 3K + 5L = 1500.

(a) Work out the first-order partial derivatives of the Lagrangian function
g(K, L, l) = 80KL + l[1500 − 3K − 5L]
(b) Find values of K and L which maximise output and satisfy the budgetary constraint.
(c) Estimate the increase in optimal output which results when the total budget of 1500 is increased to 1501.