I don't understand how it went from substituting into the production function to l = 5/8

5. The production function is F(L, M)= 4 10.5M0.5, where L is the number of units of labor and M is the number of machines. If the amounts of both factors can be varied and if the cost of labor is L.E. 64 per unit and the cost of using machines is L.E. 1 per machine, then the total cost of producing 20 units of output is a. L.E. 80. b. L.E. 650. C. L.E. 20. d. L.E. 320. e. L.E. 40. Solution: C (y = 20) = LWL + M WM MPL WL (4) 0.5 L-0.5 M0.5 64 MPM WM (4) 0.5 L0.5 M-0.5 M T = 64 M = 64L Substitute in the production function 4 L 0.5 ( 64 L ) 0.5 = 20 5 L = M* = 64 L* 64 () = 40 C (y = 20) = L WL + M WM = 64 () + 1 (40) = 80