Kindly help me to solve the following

The following production function describes the output of a local Pittsburgh mime troupe's performances given the labor of its performers: q = 217 where q denotes the hours of performances provided and I denotes hours of labor input by performers. The troupe is a price-taker both for performances (which sell for P) and for performers (which can be hired at the wage rate of w per hour). What is the total cost function [C (q)] for the troupe? b. Solve for the profit maximizing number of performer hours [(P, w)], i.e., the troupe's demand for labor. What is the profit function [x(P, w)] for this troupe? Describe the homogeneity of the profit function with respect to P and w. C. What is the supply function [q(P, w)] for the troupe's mime performances? d Use the envelope theorem (Shephard's Lemma) and the profit function you found in part (b) to double check your derivation of the troupe's demand for labor function [1(P, w)].3. True or False? Explain. (a) The utility function given by U(A, B) = (A 3)2 represents pref- erences consistent With the six assumptions about preferences as dis- cussed in class. (b) The utility function given by u(:1:1,:122) = as? | 3:2 represents prefer- ences consistent with the six assumptions about preferences as dis cussed in class