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

1. [30 POINTS] Consider the production function y = f(L,K) = 4L1/2K1/4 where L is labor and K is capital. Price per unit of the labor is w, price per unit of the capital is r, and the price per unit of the output is p. (a) [10 POINTS] 1n longrun, if the rm's objective is to maximize its prot, what are the factor demand mctions of labor and capital? (b) [10 POINTS] What is the optimal output level 3; and the maximum prot. (c) [10 POINTS] If u: = 3, r = 15 and p = 15, calculate the optimal inputs and output quantities and the maximum prot. Does the rm will stay in business or stop the production