1. Total cost function for a firm is given as TC = 0.04Q3 + 0,1Q2+2Q+5, and total revenue function is given as TR = Q2 - 4Q. Determine the profit function and calculate the production level which will maximize profits.
2. A firm can buy two inputs capital (K) and labor (L) at 18 per unit and 8 per unit respectively and faces the production function Q = 24K^0.6L^0.3. The firm has a budget constraint of 50,000 that it can spend on hiring of labor and capital.

a.What is the optimal amount of labor and capital the firm should hire?

b.What is the maximum output it can produce given a budget constraint of 50,000?

c.Interpret the value of Lagrange multiplier.