The production function of a firm:

f(K,L)=Q=KL0.2K20.3L2

K=capital

L=labor

Q=output

The prices of K and L are $40 and $10. Suppose the firm is interested in maximizing output given a budget constraint of $1000.

i)Find the optimal values of capital and labor by using the Lagrangian method.

ii)Assume the firm's budget increases by 20 percent, calculate the increase in output given the new budget