一道关于经济计量数学统计的基础题（请给详细过程）
Consider a firm with production function given by:
Q=k^0.75*L^0.25 (^代表次方）
where Q is output,K is capital input &L is labour input.the firm faces unit costs of capital of £6 and labour unite costs of £3 and has £120 to spend on factor inputs.hence the firm faces the following cost constraint 6K+3L=120
a.write out the lagrangian for the maximisation problem.
b.from the lagrangian function calculate the level of L and K which maximize the firm's output and derive the level of output.
c.show that the optimum the ratio of the firms' marginal product to price is the same for all input.
中文英语不限.