assume that a profit maximizing firm's production function function is Q=50(K^0.8)(L^0.2), where K is capital and L is labor. The firm sell its product at a competitive price$1 and hire labor at wage $40 and capital at rent$80, wtth a budget of $400.

a. Set up the firm's constraint

b. Use Lagrangian method to solve for the firm's profit maximizing capital,labor and output.

c. Solve for the Lagrange multiplier and interpretit.