The following production function describes the output of a local Pittsburgh mime troupe's performances given the labor of its performers: q:2l% where q denotes the hours of performances provided and l 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). a. What is the total cost function [C(q)] for the troupe? b. Solve for the profit maximizing number of performer hours [l(P, w)], i.e., the troupe's demand for labor. What is the profit function [7t(P, w)] for this troupe? Describe the homogeneity of the profit function with respect to P and w. 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 [l(P, w)]. P