A firm has the following constant elasticity of substitution production function:

?=100[0.2K^0.5+0.8L^0.5]^2

The firm faces a budget constraint given by10K+4L=4100

a. Write the Lagarangian function you would use to maximize the firm's production subject to their budget constraint.

b. Solve for the optimal values of K and L that would maximize output subject to the constraint.

c. Compute the value of the Lagrange multiplier and provide an interpretation for this parameter.