Please help solve the attached question with steps. Thank you~

3. [20 POINTS] Suppose that you have the following production function: Q = LK 0.4L2 0.2K2 The prices per unit of L and K are $10 and $25 respectively. Suppose you are interested in maximizing output given a budget constraint of $1000. (a) [5 POINTS] Write down the Lagrangian associated with this optimization. (1)) [10 POINTS] Solve for the optimal values for K and L. (c) [5 POINTS] Assuming that your budget was increased by 10%, calculate (approximately) the increase in output given the new budget