here is the question

A firm has the production function Q = 2K1/4 L3/4 where Q is output produced in units per period of time, K is capital input used in units per period of time, and L is labour input used in units per period of time. The firm faces the following cost (C) function P. K + PLL = C where Pr is the unit price of capital and is equal to $100; PL is the unit price of labour and is equal to $10. i) Suppose the firm has set aside $100,000 as expenditure outlay for producing Q per unit of time. By setting up a Lagrangian find the values of K and L that maximize the value of Q. What is the maximum value of Q? Be sure to verify that your second-order condition is satisfied. ii) Return to the original problem (i.e., return to the information given to you in the paragraph preceding i)). Suppose you are given the maximum value for Q (i.e., what you found as the answer to part i). Set up a constrained cost minimization problem and use your Lagrangian to find the minimum cost of producing this value of Q. Again, be sure to verify that your second- order condition is satisfied