Two firms, Tac-Burger Ltd. and Back-rib-Burger Ltd., use the same technology to produce output that is given by:

Q = 600(F^1/2 + M^1/3) K where F = Female worker; M = Male worker; K = capital

With the price of good (P) set at $1, Tac-Burger pays female an hourly wage W_F and male a wage W_M. The price of capital (r) is $1 and the quantity of capital is fixed at 1. Back-rib-Burger pays a wage W to both male and female.

a. The Press went after Tac-Burger accusing the company of gender discrimination. The CEO replied that their company was in the business to make money and their remuneration policy is consistent with the basic theory of profit maximization taught in basic principles of economics and managerial economics. What convincing argument must be put forward by the press to show that Tac-Burger indeed practices gender discrimination? What proof should the CEO provide to convince the public that the wage practice is fair?

b. Suppose W_f = $20, W_M = $30, and W = $25, how many male and female workers will each company hire?

c. What is the maximum profit obtained by each company?

d. What is the profit maximizing output level of each company?

e. Based on the mix of employees at each company in (b), can you concur with the Press that Tac-Burgers male female ratio is a result of gender discrimination

Using the Lagrange maximization technique explain each question.