A constant elasticity of substitution (CES) production function is one with the general form

where K is capital expenditure; L is the level of labor; and A, α, and β are constants that satisfy A > 0, 0 −1. Exercises 31 through 33 involve such production functions.

Use the method of Lagrange multipliers to maximize the CES production function

subject to the constraint 

2K + 5L = 150

Q(K, L) = A[aKB + (1 - a)L-B-1/